Bring sauce to room temperature. In a large bowl, whisk together ricotta, egg yolks, Parmesan, 1 1/2 teaspoons salt, black pepper, nutmeg, and cayenne pepper. Chill filling until ready to assemble lasagna.
Preheat oven to 400 degrees. Butter an 11-by-14-by-3-inch lasagna baking pan. Bring a large pot of water to a boil. Add olive oil and remaining tablespoon of salt. One at a time, add lasagna noodles; cook until very al dente, 2 to 3 minutes less than the manufacturer's instructions. Remove noodles with tongs; drain in a colander.
Spread about 3 cups of sauce on the bottom of the prepared baking dish. Place a single layer of lasagna noodles over the sauce, overlapping them slightly. Spread about 2 cups sauce over the noodles and about half the ricotta filling mixture over the sauce.
Top with a layer of lasagna noodles, again slightly overlapping them. Repeat with more sauce and remaining ricotta filling mixture. Top with a final layer of lasagna noodles. Spread a layer of sauce over the noodles, and finish with a layer of sliced mozzarella rounds.
Bake until the sauce is bubbling and the cheese is melted, at least 1 hour. Cover with aluminum foil if the cheese starts to brown too early. Let the lasagna stand 10 to 15 minutes before serving.
Cover, unbaked, and refrigerate up to one day in advance, or freeze, unbaked, up to three weeks in advance. Defrost it overnight in the refrigerator; bake as directed.