Bring a large pot of water to a boil and cook the pasta according to the package instructions until al dente.
In a small bowl, combine all the chicken seasonings: paprika, oregano, garlic powder, thyme, salt, and black pepper, mixing well.
Gently pound the chicken breasts to slightly thin them out.
Season both sides of the chicken evenly with the seasoning mixture.
Heat the olive oil in a large skillet over medium heat.
When the oil is hot, sear the chicken for 5 minutes on each side.
After searing both sides, reduce the heat to medium-low, cover the skillet with a lid, and cook the chicken for an additional 10–12 minutes.
Once the internal temperature reaches 165 degrees Fahrenheit, remove the chicken from the pan and place it on a cutting board.
Add the butter to the same pan and allow it to melt.
When melted, stir in the dry shallots, garlic powder, and Italian seasoning.
Cook and stir the seasonings for about one minute to release their aroma.
Next, sprinkle in the gluten-free flour and stir thoroughly, scraping the bottom of the pan to combine.
Pour in the chicken broth and heavy cream, whisking continuously until the sauce is smooth and creamy.
Add the shredded Parmesan cheese and stir until fully melted and incorporated.
Let the sauce cook, stirring occasionally, until it reaches your desired thickness.
Add the cooked pasta to the sauce and toss well to coat evenly.
Gradually add the reserved pasta water, one tablespoon at a time, to thin the sauce as needed.
Slice the chicken breasts and add them to the pasta.
Gently stir to combine, then serve immediately.