1. To cook pasta, add salt and 1 pound lasagna noodles (cook fresh noodles in batches of four) to a large pot of boiling water. Cook, stirring occasionally, until barely tender, 1 to 2 minutes for fresh or 6 to 8 minutes for dried. With tongs, transfer noodles to a bowl of very cold water to stop the cooking. Separate any that are stuck together. Lay noodles flat on baking sheets lined with clean kitchen towels; pat dry.

2. Preheat oven to 425 degrees, with rack in top third. Butter a 9-by-13-by-2-inch ceramic or glass baking dish; cover bottom with a layer of noodles. They should fit snugly but not overlap. Trim to fit dish.

3. Spread 1 1/4 cups ragu over noodles. Drop 2/3 cup bechamel in dollops over ragu. Gently spread bechamel with a rubber spatula. Sprinkle with 1/4 cup grated Parmigiano-Reggiano cheese. Repeat these layers three times.

4. Top with a layer of noodles. Spread 1/3 cup bechamel on top; sprinkle with 1/3 cup cheese. Season with freshly ground pepper, and drizzle with olive oil. Bake until the lasagna is golden brown and bubbling, about 25 minutes. Let stand 10 minutes before cutting with a serrated knife.