Mince the garlic cloves and thinly slice the shallot. Chop the sun-dried tomatoes into ½-inch strips and tear the fresh basil by hand to prevent bruising—I find this keeps the basil from turning black. Place the all-purpose flour in a shallow bowl and season it lightly with salt and pepper. Coat the chicken pieces in the flour, shaking off any excess; this creates a light crust that helps seal in moisture during searing.
Heat 1.5 tablespoons olive oil and 1 tablespoon butter in a large pot or Dutch oven over medium-high heat until the butter foams. Add the floured chicken pieces and sear for about 5 minutes, stirring occasionally, until golden brown on all sides. Remove the chicken to a plate and set aside. Reduce heat to medium and add the remaining 1 tablespoon butter to the pot. Add the sliced shallots and cook for 1 minute until softened, then add the minced garlic and cook for another minute until fragrant.
Stir the tomato paste into the shallot and garlic mixture and cook for 2 minutes, allowing the tomato paste to caramelize slightly and deepen in color—this builds a richer, more complex flavor foundation. Add the Italian seasoning and red pepper flakes, stirring to coat everything evenly. Pour in the chicken stock and bring the mixture to a boil, scraping any browned bits from the bottom of the pot.
Add the pasta directly to the boiling sauce and stir well to prevent sticking. Maintain a gentle boil and cook for 10-12 minutes, stirring occasionally, until the pasta is just tender and has absorbed some of the broth. I like to taste a piece of pasta around the 10-minute mark to ensure it's cooked to my preference without being mushy.
Reduce the heat to medium-low and stir in the cream, Parmesan cheese, and chopped sun-dried tomatoes from Step 1. Continue stirring until the sauce thickens and becomes creamy, about 2-3 minutes. Return the seared chicken from Step 2 to the pot and stir gently to combine, ensuring everything is coated in the rich cream sauce and heated through.
Stir in the fresh spinach and cook for about 1 minute until just wilted. Remove the pot from heat and gently fold in the torn fresh basil from Step 1, reserving a small handful for garnish. Taste and adjust seasoning with salt and pepper as needed. Divide among bowls and top with the reserved fresh basil and extra Parmesan cheese.