In a medium bowl whisk together garlic powder, onion powder, paprika, 1/4 tsp salt and 1/4 tsp pepper to make the chicken seasoning. Rub both sides of the chicken with 1/2 tablespoon sun-dried tomato oil and half the seasoning; flip and repeat with remaining oil and seasoning. Let rest while you prepare other ingredients.
Bring a large pot of salted water to a boil and cook the pasta until al dente according to package directions. Reserve 1 cup pasta cooking water, then drain and toss the pasta with a little oil to prevent sticking; set aside.
Heat 2 tablespoons sun-dried tomato oil in a very large skillet over medium-high heat until hot. Add the chicken and cook undisturbed 3–4 minutes until browned on the first side. Flip, cover, reduce heat to medium and cook 3–5 more minutes until cooked through. Transfer chicken to a cutting board, tent with foil, and keep the pan drippings in the skillet.
To the same skillet over medium-low heat add 1 tablespoon sun-dried tomato oil and 2 tablespoons butter. Add chopped shallot and sun-dried tomato strips and sauté 3–4 minutes until shallot is tender, scraping up browned bits. Add minced garlic and red pepper flakes and cook 30 seconds.
Sprinkle in 3 tablespoons flour and cook, stirring, for 1 minute. Gradually whisk in chicken broth, milk, and heavy cream until smooth. Stir in chicken bouillon, dried basil, oregano, parsley, and the remaining 1/4 tsp salt and 1/4 tsp pepper. Increase heat to medium-high and bring to a simmer, stirring often, until sauce thickens.
Reduce heat to low and stir in 3/4 cup Parmesan until melted, then add 1/3 cup mozzarella and stir until melted and smooth.
Add the drained pasta to the sauce and toss to coat. Stir in the chopped spinach and add reserved pasta water a little at a time to reach desired consistency.
Slice or chop the rested chicken and add to the pasta, stirring to combine. Taste and adjust seasoning with salt, pepper, or red pepper flakes. Garnish with additional freshly grated Parmesan and serve.
