Combine tuna and olive oil, garlic, anchovy paste, oregano, and red pepper flakes in a large saucepan over medium-low heat. Stir and cook for 1 minute once oil begins to sizzle.
Stir in cream of tomato soup and water. Increase heat to medium and simmer for about 10 minutes.
Fill a large pot with lightly salted water and bring to a boil. Stir in penne, and return to a boil. Cook pasta uncovered, stirring occasionally, until just slightly undercooked, about 11 minutes; drain.
Stir cooked pasta into soup mixture; stir in 2/3 cup Parmigiano-Reggiano cheese, and tarragon. Cover and cook for 2 minutes.
Season with salt and black pepper to taste. Cover and cook for an additional minute.
Garnish with additional Parmigiano-Reggiano cheese and red pepper flakes.