Bring a large pot of salted water to a boil, add 8 ounces of dried pasta, and cook al dente according to the package directions. Reserve ½ cup of pasta water and drain. Set it aside.
While the pasta is cooking, pat dry and cut 1 ½ pounds chicken breasts into 1-inch cubes. Place it in a bowl with 1 teaspoon kosher salt, ½ teaspoon of black pepper, and 4 tablespoons of all-purpose flour. Toss to coat thoroughly.
Heat 2 tablespoons of olive oil in a large skillet over medium-high heat until it shimmers.
Place the prepared chicken, shaking off any excess flour, in the skillet, making sure not to overcrowd. You may need to saute in two batches. Cook until lightly golden browned, for 2-3 minutes per side, adjusting the heat as necessary to ensure they are evenly browned and register 165 degrees F when inserted with a meat thermometer. Transfer them onto a plate, cover with foil, and set aside.
Add the remaining one tablespoon of olive oil and 3 cloves of minced garlic in the now-empty skillet over medium heat. Saute, stirring constantly, for 30 seconds until fragrant.
Slowly pour 2 cups of chicken stock and 1 cup of heavy cream, then add ½ cup of sun-dried tomatoes. Stir, scraping the brown bits at the bottom of the skillet with a wooden spoon. Bring it to a boil and let it simmer for 2-3 minutes.
Add the reserved chicken and simmer for 3-4 minutes, stirring frequently until slightly thickened. At this point, it should still be quite thin, but if yours gets too thick, add a splash of the reserved pasta water (or one tablespoon at a time) until it reaches your desired consistency.
Stir in ⅔ cup Parmesan cheese, ¼ teaspoon of oregano, ¼ teaspoon of thyme, 2 tablespoons of lemon juice, and ½ teaspoon of red pepper flakes, if using. Taste and adjust seasoning.
Add the cooked pasta to the sauce and toss well to combine. Let it simmer for 3-4 minutes to warm thoroughly.
When serving, sprinkle with additional Parmesan and torn basil.