Bring a large pot of lightly salted water to a boil. Cook pasta in boiling water until al dente, adding peas for the final 3 minutes of cooking; drain.
Melt the butter in the same pot over medium heat. Add the mushroom soup, tuna, milk, and Cheddar cheese. Stir until cheese is melted, and the mixture is smooth. Stir in the pasta and peas until evenly coated.