Bring a large pot of salted water to a boil. Cut the cardoons into 3-by-1-inch pieces and add them to the pot, along with the wine, thyme and lemon, and cook until the cardoons are tender, 1 hour. Drain, discarding the lemon and thyme sprigs, and let cool.
Line up three shallow dishes and fill with the flour, eggs and bread crumbs, respectively. One at a time, dredge the cardoons in the flour, egg and bread crumbs, then egg and bread crumbs again. Transfer each to a plate until ready to fry.
Meanwhile, in a 6-quart Dutch oven, heat 2 inches of oil to 350 F. Line a plate with paper towels and set aside. Working in batches, fry the breaded cardoons until golden brown, 1 to 2 minutes. Transfer to the prepared plate to drain, immediately seasoning with salt. Garnish with grated Parmesan and chopped parsley, then serve with lemon wedges.