Preheat oven to 375 degrees.
Grease 9x13" baking pan with 1 tbsp.butter.
Cover dried tomatoes with 1 cup boiling water; soak for 20 minutes. Drain. Chop. Set aside.
Make bechamel sauce: heat 8 tablespoons butter in a 4 quart saucepan over medium heat. Add shallots and carrots; cook for 5 minutes. Add flour; cook two minutes. Whisk in milk; boil. Reduce heat to medium-low; simmer, whisking, until thick, 20-25 minutes. Season with salt and pepper.
Meanwhile, heat olive oil and remaining butter in a 6 quart pot over medium-high heat. Add mushrooms; cook 10 minutes. Add dried tomatoes, spinach, garlic, parsley, oregano, thyme, rosemary, and tomato paste; coo 3 minutes. Add canned tomatoes. Cook for 8-10 minutes, stirring occasionally. Set sauce aside.
Spread 2 cups of tomato sauce in baking dish. Cover with a layer of noodles (uncooked). Spread 1 cup bechamel sauce over top; sprinkle with 1/2 cup of each cheese and 2 cups tomato sauce. Repeat layering 2 more times.
Top with remaining noodles, tomato sauce, bechamel, and cheeses.
Bake, covered with foil, on a baking sheet for 1 hour. Remove foil; raise oven temp to 500 degrees. Bake until golden, 15 minutes.
Allow to stand 15-20 minutes before cutting into servings.