Heat 2 tablespoons of olive oil in an 8-inch skillet over medium-high heat.
Add the diced potatoes, season with salt, and cook, stirring occasionally, until tender and lightly browned, about 15 minutes.
Transfer to paper towels to drain excess oil.
In the same skillet over medium heat, add the remaining tablespoon of olive oil.
Cook the sliced bananas until they're lightly browned.
Transfer them to paper towels to drain excess oil.
Set aside and clean the skillet.
In a mixing bowl, lightly beat the eggs, season with salt, and let the diced potatoes sit in the egg mixture for 5 minutes.
Stir in the cooked bananas.
Heat the skillet over medium-high heat, adding a teaspoon of olive oil if needed.
Pour in the egg mixture, spreading it evenly.
Cook until the edges and bottom begin to brown, and the center is mostly set but still slightly moist.
Slide the omelet onto a plate, cover it with another plate, and carefully flip it over.
If the skillet is dry, add a teaspoon of oil, then return the omelet to the skillet.
Cook until the center is fully set but still retains some juiciness.