In a bowl, dissolve the yeast in the lukewarm water. Add the salt and set aside until it begins to foam and bubble. Gradually add the flour and mashed potatoes, mixing until the dough forms a sticky ball. Add 1 1/2 tablespoons of the olive oil.

Coat a bowl with 2 tablespoons of the olive oil. Place the dough in the bowl and turn to coat with olive oil.

Cover with a damp cloth and let rise in a draft-free place for 25 minutes.

Punch down with the dough and place on a baking sheet coated with 1/2 tablespoon olive oil.

Shape it into a 1/2-inch thick round or oval.

Randomly press the olives into the dough.

Sprinkle with the remaining 3 tablespoons olive oil, the goat cheese, and rosemary.

Allow to rest for 20 minutes.

Preheat the oven to 400°.

Bake the focaccia for 30 minutes, or until golden.

Serve warm.