Arrange a rack in the middle of the oven and heat the oven to 400°F. Meanwhile, arrange 15 dry lasagna noodles in an even layer in a 9x13-inch baking dish. Cover the noodles with hot tap water and let soak while you prepare the filling and sauce, about 30 minutes.

If using frozen spinach, thaw 16 ounces according to package directions. Transfer to a clean kitchen towel, roll it up in the towel, and carefully squeeze out all the excess moisture.

Heat 1 tablespoon olive oil in a large Dutch oven or pot over medium-high heat until shimmering. Add 1 pound uncooked Italian sausage and cook, breaking it up with a wooden spoon, until browned and cooked through, 5 to 7 minutes. Add 1 diced onion and 3 minced garlic cloves, and cook, stirring occasionally, until softened and translucent, about 5 minutes.

If using fresh baby spinach, add 1 pound a few handfuls at a time and stir until just wilted, 3 to 5 minutes. If using frozen spinach, add to pot and cook, stirring occasionally, until the liquid has evaporated, about 2 minutes. If necessary, drain off any liquid. Season with ½ teaspoon of the kosher salt and ¼ teaspoon of the black pepper. Remove the pot from the heat and let cool while you make the béchamel sauce.

Melt 1 stick unsalted butter in a large saucepan over medium heat. Add ½ cup all-purpose flour, and cook, whisking constantly, until the paste is bubbling and begins to dry out slightly, about 2 minutes. Gradually whisk in the milk until no lumps remain. Bring to a boil over high heat. Reduce to a simmer, and cook, stirring occasionally, until thickened, 1 to 2 minutes. Add 2 teaspoons of the kosher salt and a pinch of ground nutmeg, and stir to combine. Remove the pot from the heat.

Place half of the Parmesan cheese, 1 container ricotta cheese, the remaining ¼ teaspoon kosher salt, and remaining ¼ teaspoon black pepper in a medium bowl and stir to combine. Drain the lasagna noodles.

Assemble the lasagna: Place ¼ cup béchamel sauce into the baking dish and spread into a thin, even layer. Arrange 5 of the lasagna noodles in an even layer on top of the sauce, breaking them if needed to fit (it’s OK if the noodles overlap slightly). Dollop and spread ½ of the ricotta mixture over the noodles. Spoon ½ of the sausage and spinach over the ricotta. Sprinkle with 1 cup of the mozzarella. Dollop and spread about 1 heaping cup of the béchamel over the mozzarella.

Repeat layering 5 more lasagna noodles, the remaining ricotta mixture, the remaining sausage and spinach, 1 cup of the mozzarella, and 1 heaping cup of the béchamel. Top with the remaining lasagna noodles, remaining béchamel sauce, remaining mozzarella, and remaining Parmesan.

Bake uncovered until the cheeses are melted and lightly browned, and the sauce is bubbling, about 30 minutes. Let cool on a wire rack for at least 15 minutes before serving.