Preheat the oven to 350 degrees F.

Bring 6 quarts of water to a boil, add 2 tablespoons salt and lemon juice.

Remove the cardoons from the acidulated water, rinse and cook in the boiling water until tender but not fully cooked, about 30 minutes. Drain well and dry on paper towels. Dredge each cardoon in the flour, then the eggs.

In a 14-inch saute pan, heat about 1/2 cup of oil over high heat until almost smoking. Fry the cardoon pieces in the oil until golden brown, working in batches to avoid overcrowding the pan. Drain the cardoons on a plate lined with paper towels. Season with salt and pepper. Meanwhile, heat the tomato sauce in a small saucepan until bubbling. When all cardoons are cooked, place in a casserole with the hot sauce and the grated cheese. Distribute the butter evenly across the top of the dish and bake in the oven 15 minutes.