Classic Italian Lasagna

5 tablespoons unsalted butter, plus 2 tablespoons for the lasagna 1/2 cup all-purpose flour 4 cups whole milk at room temperature Pinch freshly grated nutmeg 1 1/2 cups tomato sauce, recipe follows Salt and white pepper 1/4 cup extra-virgin olive oil 1 pound ground chuck beef Salt and pepper 1 1/2 pounds ricotta cheese 3 large eggs 1 pound lasagna sheets, cooked al dente 2 packages (10 ounces each) frozen chopped spinach, thawed and squeezed dry 3 cups shredded mozzarella 1/4 cup freshly grated Parmesan