I ended up ditching the default export:

// UniqueIdGenerator.js
export const uniqueIdGenerator = () => Math.random().toString(36).substring(2, 8);

And then I could use and spy it like this:

import * as UniqueIdGenerator from './UniqueIdGenerator';
// ...
const spy = jest.spyOn(UniqueIdGenerator, 'uniqueIdGenerator');

Some recommend wrapping them in a const object, and exporting that. I suppose you can also use a class for wrapping.

However, if you can't modify the class there's still a (not-so-nice) solution:

import * as UniqueIdGenerator from './UniqueIdGenerator';
// ...
const spy = jest.spyOn(UniqueIdGenerator, 'default');

The package logger is already default import so it's not supposed to have default property.

A correct way to spy on it is:

import * as loggerMod from '../../../src/Logger'
...
const loggerSpy = jest.spyOn(loggerMod, 'default');

This may not work because ES modules are read-only and whether this is enforced depends on a setup.

A more correct way is to do this in module mock:

import logger from '../../../src/Logger'

jest.mock('../../../src/Logger.js', () => {
  const loggerMod = jest.requireActual('../../../src/Logger');

  return {
    ...loggerMod,
    __esModule: true,
    default: jest.fn(loggerMod.default)
  };
});

...

expect(logger).toHaveBeenCalled();

Most times it's preferable to mock a function that does potentially undesirable side effects rather than spy on it, and this is much simpler, especially for a module with default export only:

jest.mock('../../../src/Logger', () => jest.fn());

This is the closed solution:

export function bar() {
  // do something
}

export function foo() {
  exports.bar();   // <-- have to change to exports.bar() instead of bar()
  // or this.bar(); would also work.
}

import * as utils from './utils';

describe('tests', () => {
  it('example test', () => {
    const barSpy = jest.spyOn(utils, 'bar');
    utils.foo();
    expect(barSpy).toHaveBeenCalled();
  });
});

Or take a look this duplicated question