Preheat the oven to 375 degrees F.

Prepare the Fresh Tomato Sauce: Heat the olive oil in a large skillet over moderate heat. Add the garlic and sauté until it is golden, then add the tomatoes, basil and salt to taste. Simmer until reduced to 2 cups. If the sauce tastes too tart, add a pinch of baking soda and simmer 1 minute longer. Remove from the heat and remove the basil sprig and garlic clove.

Prepare the Filling: In a bowl, stir together the ricotta, egg yolks, ham, mozzarella, Parmesan and basil. Season with salt and pepper.

Cut the pasta sheets into squares roughly 4-1/2 to 5 inches per side. You will need 16 squares. Bring a large pot of salted water to a boil. Boil the pasta until about half done, then transfer the sheets to ice water to cool quickly. Lift the sheets out of the ice water and place them on clean dishtowels.

Lightly oil a rimmed baking sheet or large baking dish. Put 1/2 cup tomato sauce at one end of the baking sheet and spread it into the shape of the pasta squares. Top the sauce with one pasta square, spread a scant 3 tablespoons filling evenly on the pasta, then continue making layers of pasta and filling until you have 8 layers of pasta alternating with 7 layers of filling. Spoon 1/2 cup tomato sauce on top of the last pasta layer, then sprinkle 1 tablespoon Parmesan and 1 teaspoon chopped parsley over the top. Repeat with remaining ingredients to make two identical lasagne.

Bake until bubbling and lightly browned, about 30 minutes. Let rest 5 minutes, then cut each lasagne in half to make 2 lasagnette. Serve immediately.