2 teaspoons sugar
1 package active dry yeast
3 tablespoons extra-virgin olive oil, plus more for the bowl
3 cups all-purpose flour, or 2 3/4 cups plus 1/4 cup whole-wheat flour, plus more for dusting
1 teaspoon fine salt
5 tablespoons extra-virgin olive oil, plus more for the pan
3 cups sliced green cabbage
Kosher salt
1 teaspoon pickling spices, tied securely in cheesecloth
1 large potato, peeled and thinly sliced
Freshly ground pepper
2 cups shredded mozzarella cheese
3/4 cup shredded monterey jack cheese
1/2 cup freshly grated parmesan cheese
6 ounces sliced corned beef