Step 1

FOR THE SAUCE: Melt butter in medium saucepan over medium-low heat. Add onion, garlic, anchovies, salt, pepper flakes, and oregano and cook until onion is softened, about 3 minutes. Stir in crushed tomatoes, diced tomatoes and their juice, and sugar; increase heat to medium-high; and bring to simmer. Reduce heat to medium-low and simmer until slightly thickened, about 10 minutes. Off heat, stir in basil and oil. Season with salt and pepper to taste. Set aside. (Sauce can be refrigerated for up to 48 hours.)

Step 2

FOR THE EGGPLANT: Cut stem end off eggplants and discard. Cut ¼-inch-thick slice from 1 long side of each eggplant and discard. Using mandoline or slicing knife and starting on cut side, slice eggplants lengthwise ¼ inch thick until you have 20 slices total (you may not need all 3 eggplants).

Step 3

Place flour in shallow dish. Beat eggs in second shallow dish. Line baking sheet with triple layer of paper towels. Heat oil in 12-inch skillet over medium heat to 350 degrees (to take temperature, tilt skillet so oil pools on 1 side). Working with 3 or 4 slices at a time (depending on size of eggplant), dredge eggplant in flour, shaking off excess; dip in egg, allowing excess to drip off; then place in hot oil. Fry until lightly browned on both sides, about 1½ minutes per side. Transfer to prepared sheet. (As eggplant slices cool, you can stack them to make room on sheet.)

Step 4

Adjust oven rack 6 inches from broiler element and heat oven to 375 degrees. Spread 1 cup sauce in bottom of broiler-safe 13 by 9-inch baking dish. Starting with largest slices of eggplant, place 4 eggplant slices side by side over sauce in dish. Spread ½ cup sauce over eggplant, then sprinkle ½ cup Pecorino over top. Repeat layering 3 times to make 4 stacks of 4 slices. Place remaining eggplant slices on top. Spread remaining sauce over top layer of eggplant, then sprinkle with fontina.

Step 5

Bake until bubbling around edges and center of casserole is hot, about 30 minutes. Broil until fontina is lightly browned, 1 to 3 minutes. Let cool for 20 minutes. Serve.

Step 6

TO MAKE AHEAD: Casserole can be assembled through step 4, without fontina, and refrigerated for up to 24 hours. When ready to cook, cover with aluminum foil and bake for 20 minutes. Remove foil, sprinkle with fontina, and continue to bake as directed in step 5.