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)

Just another way of doing it:

df = pd.DataFrame(d).T #choosing d as a name for dict because dict is a keyword
Bcols = df.columns
df = pd.concat([df[col].apply(pd.Series) for col in df.columns], axis=1)
df.columns = pd.MultiIndex.from_product([Bcols, df.columns]).drop_duplicates()
df.rename_axis('Region', axis=0, inplace=True)

print(df):

              B1              B2              B3        
       Average Max Min Average Max Min Average Max Min
Region                                                
A1           0   0   0       0   0   0       0   0   0
A2           0   0   0       0   0   0       0   0   0

The order of the loops has to be reversed.

This is what you're looking for:

D = {f'{ko}_{ki}_{i}': someFunc(ko, ki, i) for ko, vo in d.items() for ki, vi in vo.items() for i in range(vi)  }