Building a dictionary first with useful names helps to understand what is going on.

temp = {}
for year1, values1 in data.items():
    for author1, values2 in values1.items():
        for number, values3 in values2.items():
            temp.setdefault('Year1', []).append(year1)
            temp.setdefault('Author1', []).append(author1)
            temp.setdefault('No.', []).append(number)
            for key, value in values3.items():
                temp.setdefault(key, []).append(value)
print(pd.DataFrame(temp))

Output:

            Author          Author1           City  No.  \
0     Barack Obama     Barack Obama             []    1   
1     Barack Obama     Barack Obama  [Springfield]    2   
2     Barack Obama     Barack Obama      [Chicago]    3   
3  Bill Richardson  Bill Richardson             []    1   
4  Bill Richardson  Bill Richardson             []    2   
5  Bill Richardson  Bill Richardson             []    3   
6     Barack Obama     Barack Obama        [Parma]    1   
7     Barack Obama     Barack Obama     [Sandusky]    2   
8     Barack Obama     Barack Obama             []    3   



                                               Title     Type  Year  Year1  
0  Keynote Address at the 2004 Democratic Nationa...  address  2008   2008  
1  Remarks Announcing Candidacy for President in ...  remarks  2008   2008  
2       Remarks at the AIPAC Policy Forum in Chicago  remarks  2008   2008  
3  Iraq Speech to New Hampshire Democratic State ...   speech  2008   2008  
4                  Address to the DNC Winter Meeting  address  2008   2008  
5  Speech: The New Realism and the Rebirth of Ame...   speech  2008   2008  
6   535 - Remarks at a Campaign Rally in Parma, Ohio  remarks  2012   2012  
7  534 - Remarks at a Campaign Rally in Sandusky,...  remarks  2012   2012  
8  533 - Remarks at a Campaign Rally in Maumee, Ohio  remarks  2012   2012 

Our create with your desired column order:

df = pd.DataFrame(temp, columns=['Year1', 'Author1',  'No.', 'Author',
                                 'City', 'Title', 'Type', 'Year']) 
df

I've written this after I saw @VoNWooDSoN's answer. I turned it into an iterator instead of printing inside the function and a little bit of changes to make it more readable. So see his original answer here.

def flatten(d, base=()):
    for k, v in d.items():
        if isinstance(v, dict):
            yield from flatten(v, base + (k,))
        else:
            yield base + (k, v)

1- yielding instead of printing.

2- isinstance() instead of type so that subclasses of dict can also work. You could also use MutableMapping from typing module instead of dict to make it more generic.

3- IMO , getting (k, v) pairs from .items() is much more readable than k and d[k].

More generic ?

Do you wanna expand this to even more generic which CAN(not have to, like the solution in the OP) accept the number of depths just in case?

Consider these examples:

d_level1 = {"a": 1, "b": 2, "c": 3}
d_level2 = {"group_1": {"a": 1}, "group_2": {"b": 2, "c": 3}}
d_level3 = {"collection_1": d_level2}

for items in flatten(d_level3):
    print(items)
print('------------------------------')
for items in flatten(d_level3, depth=0):
    print(items)
print('------------------------------')
for items in flatten(d_level3, depth=1):
    print(items)
print('------------------------------')
for items in flatten(d_level3, depth=2):
    print(items)

output:

('collection_1', 'group_1', 'a', 1)
('collection_1', 'group_2', 'b', 2)
('collection_1', 'group_2', 'c', 3)
------------------------------
('collection_1', {'group_1': {'a': 1}, 'group_2': {'b': 2, 'c': 3}})
------------------------------
('collection_1', 'group_1', {'a': 1})
('collection_1', 'group_2', {'b': 2, 'c': 3})
------------------------------
('collection_1', 'group_1', 'a', 1)
('collection_1', 'group_2', 'b', 2)
('collection_1', 'group_2', 'c', 3)

depth=None doesn't consider the depth (still works like you want at the first place). But now by specifying depths from 0 to 2 you can see that we are able to iterate how deep we want. here is the code:

def flatten(d, base=(), depth=None):
    for k, v in d.items():
        if not isinstance(v, dict):
            yield base + (k, v)
        else:
            if depth is None:
                yield from flatten(v, base + (k,))
            else:
                if depth == 0:
                    yield base + (k, v)
                else:
                    yield from flatten(v, base + (k,), depth - 1)

You are iterating over cost as well. Try this:

#level one of the dictionary
for drink, data in MENU.items():
    #this should print the drinks and cost
    print(drink, data["cost"])
    #this should print the ingredients   
    for ingredient in data["ingredients"].items():
        print(ingredient)