Add the yeast to the warm water, stirring to dissolve. Then add 2 eggs, half the sugar and mix well. Add 1/2 cup of the flour, stirring to mix well, and adding a bit more if necessary to form a small ball of starter dough. Add half the butter, mixing to incorporate, then place the starter dough in into a lightly floured mixing bowl. Cover the bowl with a damp kitchen towel, and place in a warm spot (like above the refrigerator). Let the starter rest for 1 hour.
Place the dough into a mixer with a hook attachment. Add the remaining flour, the remaining sugar, and the remaining butter. Add the salt, and 1 egg yolk and mix again on medium for 10 minutes. Let the resulting dough rest, covered, for 5 hours.
Preheat the oven to 350 degrees F.
Lightly butter and flour a 9-inch springform pan. On a lightly floured surface, gently roll the dough out to a 8-inch circle, about 1/2-inch thick. Gently lay the dough into the center of the pan, leaving a slight border all the way around between the dough and the pan sides.
Using a fork, whisk the remaining 1 egg yolk and add 1/2 teaspoon of extra-virgin olive oil. Lightly brush the egg wash over the top of the dough. Sprinkle the almond slices over the top and place the pan in the oven. Bake until the "pizza" is a light golden brown, about 1 hour. Garnish with powdered sugar and serve.