Chicken and Shrimp Alfredo

1 (16 ounce) package trotolle dry pasta
4 tablespoons extra-virgin olive oil, divided
4 cloves garlic, thinly sliced
1 tablespoon dried basil
1/2 teaspoon red pepper flakes
1/2 teaspoon ground black pepper
2 pounds chicken breast, cut into strips
1 stick butter
1 (8 ounce) package cream cheese, cut into small pieces
2 cups milk, or more as needed
2 cups heavy cream
3 cups shaved Parmigiano-Reggiano cheese
3 tablespoons pesto
3 tablespoons sun-dried tomatoes packed in oil, drained and chopped
1/2 pound uncooked medium shrimp, peeled and deveined

Bring a large pot of lightly salted water to a boil; add 2 tablespoons olive oil.
Add trottole and cook at a boil until tender yet firm to the bite, about 8 minutes; drain.
Heat remaining olive oil in a large skillet and add garlic, basil, red pepper flakes, and black pepper.
Add chicken; cook and stir until browned, about 10 minutes.
Melt butter over medium heat in the large pot used to make the pasta.
Add cream cheese and stir until creamy, about 1 minute. Add 2 cups milk and heavy cream,
stirring until warm, about 5 minutes.
Add Parmigiano-Reggiano cheese and continue stirring.
Add more milk to thin sauce, if needed. Add pesto and sun-dried tomatoes.
Stir cooked chicken and pasta into the sauce.
Add shrimp; cook and stir until shrimp turns orange, 6 to 8 minutes more.