Bring a large pot of water to a boil over medium-high heat. Add 1 teaspoon salt and the spinach. Cook until the spinach is limp and tender but still bright green, 4–6 minutes. Drain and rinse under running cold water to stop the cooking. Squeeze dry to remove as much moisture as possible and chop coarsely. Squeeze dry again and set aside.
In a bowl, mix together the ricotta, shallots, thyme, egg, and ½ teaspoon salt. Set aside. In a saucepan over medium heat, melt the butter. When it foams, whisk in the flour, ½ teaspoon salt, the nutmeg, and the cayenne until a paste forms. Slowly whisk in the hot milk, reduce the heat to medium-low, and cook, whisking often, until the sauce is thickened, about 15 minutes. Remove from the heat.
Preheat the oven to 375°F (190°C). Pour a thin layer of the sauce in the bottom of a 9-by-13-inch (23-by-33-cm) baking dish. Add a single layer of 4 lasagne noodles. Top with one-third of the spinach, a thin layer of the sauce, one-third of the ricotta mixture, one-third of the romano, and one-fourth of the mozzarella. Repeat the layers twice, then top with the remaining 4 noodles. Pour over the remaining sauce, slipping a knife along the edges to ensure the sauce runs down into the pan. Top with the remaining slices of mozzarella. Bake until the sauce is bubbling, the top is brown, and the pasta is tender to the bite, about 45 minutes. Let stand for 10 minutes before serving. Cut into squares and serve at once.