In a large skillet, heat 1 tablespoon butter over medium-high heat. Add carrots, onion, red pepper and mushrooms. Cook and stir until tender, 8-10 minutes. Add tuna, spinach and peas; cook until spinach is just wilted, 2-3 minutes. , Meanwhile, cook pasta according to package directions for al dente. Drain pasta, reserving 1 cup pasta water. In a large bowl, place pasta and tuna mixture; toss to combine. Wipe skillet clean., In the same skillet, melt remaining butter over medium heat. Stir in flour until smooth; gradually whisk in broth and cream. Bring to a boil, stirring constantly; cook and stir until thickened, 1-2 minutes, adding reserved pasta water if needed. Stir in cheese, salt and pepper. Pour over pasta; toss to coat.