In a colander, toss eggplant with 1 1/2 teaspoons salt. Let stand 30 minutes. Press slices between a double layer of paper towels to dry and set aside.
Preheat oven to 400 degrees; place a rimless baking sheet or inverted rimmed baking sheet in oven. On a floured surface, roll out dough to 1/2-inch thickness. Sprinkle cornmeal on another baking sheet or inverted rimmed baking sheet or lightweight wooden board; top with dough (you will transfer it onto the preheated sheet to cook).
Brush dough with 3 tablespoons oil and sprinkle with 1/2 cup cheese. Layer on eggplant; top with 3 tablespoons oil, oregano, and 1/2 cup cheese. Let stand 30 minutes. Give sheet a gentle shake to ensure dough isnt sticking.
Carefully remove baking sheet from oven and slide focaccia onto sheet. Return to oven and bake until bottom of focaccia is crispy and edges are golden, 20 minutes. Serve warm or at room temperature.