Brush chicken with ½ cup of pesto, coating all sides.
To a large skillet over medium-high heat, add oil.
Once the oil is hot, add chicken and cook for 7-8 minutes on each side, or until the internal temperature reaches 165°F. (Cooking times may vary depending on the size of the chicken breasts.)
Remove the chicken from the skillet and set aside. Tent to keep warm.
In the same skillet, melt butter. Add garlic and cook 1 more minute, or until fragrant.
Add the flour and whisk, scraping up any brown bits in the pan, until the mixture is lightly browned, about 2 minutes.
Slowly pour in milk, whisking constantly. Mix in the chicken stock, cherry tomatoes, salt, pepper, and red pepper flakes. Bring the mixture to a low rolling boil and then reduce heat and simmer, stirring occasionally, until thickened (about 5 minutes).
Remove from heat. Add in the remaining pesto, mozzarella, and parmesan cheese. Stir until the cheeses are melted. Mix in the cooked pasta.
Slice chicken, add to the top of the dish, and mix in with the rest of the ingredients. Salt to taste. Garnish with basil.