This recipe is a little more work than the standard lasagna, but much of it can be made ahead.
Ragu
Heat oil in a skillet. Brown beef, carrots, celery, and onion until beef is cooked. Stir in red wine and tomato sauce. Simmer 5 minutes or more until almost all liquied has evaporated. Season with salt and pepper. Can be made 3 days ahead. Keep refrigerated.
Bechamel
Melt butter in large saucepan over mEdium heat. Add flour and cook 3 minutes, stirring frequently. Gradually whisk in milk until thickened, about 5 minutes. Can be made 1 day ahead. Keep refrigerated.
Lasagna
Preheat oven to 400 F.
Cook lasagna noodles in boiling salted water until tender but stlll firm to bite. Drain and rinse under cold water. Butter bottom and sides of glass baking dish. Cover bottom of dish with noodles. Spread 1/2 cup bechamel over noodles. Spread 1 cup ragu over bechamel. Sprinkle with 1/4 cup Parmesan. Repeat 3 more times. Ending with bechamel and cheese.
Can be made 8 hours ahead.
Bake lasagna until bubbling at edges and golden, about 45 minutes.
While lazagne is baking, heat skillet with butter. Add washed spinach. Cook, stirring often until spinach is wilted.
Top lasagna with spinach and serve.