Add sugar and yeast to 1 1/8 cup of very warm water. Set it aside until it begins to foam (about 10 minutes). If it doesn't foam, that means that your yeast is dead and you will need to get new yeast. This step is called "proofing your yeast."
Add your flour, mashed potatoes, garlic, Italian seasoning, 2 teaspoons of salt, and 1/4 cup of extra virgin olive oil into a large bowl.
Using a large spoon, begin mixing the contents until a very rough dough forms, about 2 minutes.
Flour your working surface with up to 2 tablespoons of flour (use as little as you can get away with). Empty the contents of your bowl onto your surface and begin kneading the dough by folding a section into the middle, pressing it with the heel of your hand, rotating the dough 45°, and repeating (watch video below). Knead for about 5 minutes and form the dough into a rough ball.
Place the dough ball back into the bowl (which you should have cleaned) and stick the bowl in a fairly warm place (78° F if you're using a bread box) until your dough doubles in size, between 60 to 75 minutes (this is your first "proof").
Slice a Yukon gold potato into thin slices. Place the slices into a bowl with some salt and cold water.
Add 1/4 cup of extra virgin olive oil to a baking pan 9 x 13 inch baking pan OR a round pan with a 13-inch diameter (as pictured above).
Place the dough into the pan (it will be sticky). Cover the pan and place it back in that warm spot you proofed it the first time for another 45 minutes (this is your second "proof").
Preheat your oven to 400°F.
Once the dough has finished proofing a second time, remove the potato slices from water and pat them dry, as thoroughly as possible, with a kitchen towel.
Arrange the potato slices in one layer over the dough.
Drizzle a little more olive oil (or none--it's up to you) over the potatoes and sprinkle generously with sea salt.
Place the dough into the oven and bake for approximately 35 minutes, until the potatoes are golden brown.