4 medium green tomatoes, cored and cut into ¼-inch-thick slices
2 large eggs, lightly beaten
1 cup panko
1 cup freshly grated Parmesan cheese, plus more for serving
2 tablespoons olive oil, plus more if needed
2 tablespoons unsalted butter, plus more if needed
Freshly ground black pepper
Lay the tomato slices on a baking sheet and sprinkle generously (like you’re seasoning a steak) with both salt and sugar. Turn over the slices and season the other sides. Let sit for 30 minutes. Have a large non-stick sauté pan on the stove. Add the beaten egg to a wide shallow bowl. Combine the panko and Parmesan in another wide shallow bowl. Set them near the stove. Lay the tomato slices on paper towel, top with another layer of paper towel and press on the tomatoes to dry them well. Season the slices again with a little salt. Working one at a time, dip the tomatoes in egg, then the panko-Parmesan mixture. Really press and pat the panko into the tomatoes. Set the tomatoes on a clean baking sheet. Heat the sauté pan over medium-high heat, and add the olive oil and butter. When the foam subsides, add the tomatoes, enough to cover the base of the pan in a single layer. Let them be for a few minutes and when you see browning on the egde, check the tomatoes. You want a nut brown crust. Turn them and brown the other side. Keep working in batches, adding more oil and butter to the pan as needed, and transfer the tomatoes to a warm serving platter. Grind (coarsely!) fresh pepper on top, sprinkle with extra cheese, and serve!