That won't even work within the EU. All sorts of barriers exist between EU states making this extremely difficult if not impossible.

You'll need a salary or other reliable income sources in the EU member state where you're buying, banks there won't offer you a mortgage. Never mind you're earning 5 times the bank employee's salary, just in another member state.

You'll need free and clear ownership of a home in the EU member state where you're earning, or banks there won't offer you a mortgage for your home in another EU member state. You'll only get the loan by mortgaging the property local to the bank, not the actual property you're buying.

Some limited exceptions exist for popular holiday countries, but banks will make you pay for that "privilege".

That exposes you to currency risk. Right now, 1 euro trades for about 1.23 dollars but that can go up or down (1:1.12 a year ago for example) which would effect your payments over the life of the loan because I get paid in dollars but german banks want to get paid back in euros.