For the stewed fennel and tomatoes: Preheat the oven to 350 degrees F. Combine the tomatoes, onions, red and yellow bell peppers, white wine, basil, oil, oregano, salt, black pepper, garlic and fennel in a shallow baking dish and stir gently. Bake until the fennel is tender and the liquid has reduced by almost half, 45 minutes.
For the artichokes: Bring 3 liters water, the lemon juice and salt to a boil, and cook the artichokes until just becoming tender, 5 to 6 minutes. Remove and let cool.
For assembly: Lay half of the tomato and fennel with 1/4 cup water on the bottom of a shallow baking dish large enough to hold the artichokes without overcrowding them. Place the artichokes hollow-side up on top. Spoon 1 tablespoon of the remaining tomato and fennel into the artichokes, and then top each one with a raw, unbroken egg yolk. Cover the dish with foil and bake, 10 minutes. Remove the foil, sprinkle the Parmesan over the artichokes, and then return to the oven until the cheese is melted, another 3 minutes.
To plate: Spoon some of the tomato and fennel onto a plate. Place an artichoke on top, taking care as they are very delicate at this point, and cut in half, revealing the creamy egg yolk. Serve both halves on the plate, garnished with fresh basil leaves, drizzled olive oil and fresh Parmesan shavings.
This recipe was provided by a chef, restaurant or culinary professional and may have been scaled down from a bulk recipe. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.