Roast the peppers: Preheat the broiler. Place the peppers on a baking sheet and broil 2 to 3 inches from the heating element, turning them occasionally, until wrinkled and charred, 10 to 15 minutes. Remove the peppers from the broiler, transfer to a bowl, cover with foil or plastic wrap, and let cool.

When the peppers are completely cool, peel away the skins as delicately as possible. Cut a vertical slit in each pepper and remove the core and seeds, keeping the peppers intact, ideally with the stems. (Don't be tempted to rinse the peppers as you peel them, which would wash away flavorful juices.)

Put the sheep's-milk cheese, farmer's cheese, kashkaval, ricotta, and Parmesan, if using, in a medium bowl and stir to blend thoroughly.

Beat the eggs with the salt and pepper in a shallow bowl. Put a mound of flour on a plate. Line another plate or small tray with paper towels.

Gently coat one pepper on all sides with flour, shaking off any excess. Place a heaping teaspoon (or two, depending on the size of your pepper) of filling into the pepper and very gently wrap the pepper around it to close. Generously flour the pepper again and place on a plate or wire rack. Repeat with the remaining peppers.

Fill a large deep skillet or wide saucepan with ¼ inch of oil and heat over medium-high heat. Add the butter and garlic clove. When the garlic begins to sizzle, dip one of the stuffed peppers in the beaten eggs, gently turning to coat on all sides, and carefully place it in the hot oil. Repeat with a few more stuffed peppers, being careful not to overcrowd the pan; you'll probably need to cook the peppers in two or more batches. Reduce the heat to medium; the peppers should sizzle and the oil should form small bubbles around them. Turn the peppers gently after 2 minutes, and then again after 2 more minutes. After another 2 minutes, so the peppers have fried on three sides, for a total of 6 minutes, carefully remove them from the pan and place on the plate lined with paper towels.

Serve the peppers immediately, while the coating is still crisp.