In a large saucepan, heat the olive oil over medium heat. Add the garlic and cook until fragrant, about 1 minute. Add 2 tablespoons parsley and cook for 1 minute. Add the tomatoes and season with salt and pepper. Cook over low heat until the sauce thickens, about 20 minutes. Whisk in the butter, then stir in the tuna.
Meanwhile, in a large pot of boiling, salted water, cook the pasta until al dente; drain. Add the pasta to the tuna sauce and stir in threequarters of the remaining parsley; season with salt and pepper. Top with the remaining parsley.