Pat chicken thighs dry with paper towels. Combine salt, pepper, garlic powder, and smoked paprika; season both sides of each thigh. Heat olive oil in a 12-inch stainless steel skillet over medium-high until shimmering.
Add chicken smooth-side down. Sear undisturbed 4 to 5 minutes until deeply golden and releasing cleanly. Flip and sear 3 to 4 more minutes. Transfer to a plate; the chicken doesn’t need to be fully cooked yet.
Start a large pot of generously salted water and bring to a boil for the pasta.
Reduce skillet heat to medium. Add garlic to the fond in the pan; stir 60 seconds until golden. Add tomato paste to the center; cook undisturbed 30 to 45 seconds until brick-red, then stir through. Add sun-dried tomatoes, oregano, thyme, and chili flakes; cook 60 seconds.
Pour in chicken broth, scraping all fond from the pan base. Add heavy cream and stir to combine. Bring to a gentle simmer and cook uncovered 4 to 5 minutes until the sauce coats a spoon.
Nestle chicken back into the sauce. Simmer on medium-low 8 to 10 minutes, basting twice, until chicken reaches 74°C (165°F) at the thickest point.
Meanwhile, cook pasta to al dente. Reserve 1 cup pasta water before draining.
Remove pan from heat. Remove chicken; rest 3 minutes. Stir Parmesan into the sauce in two additions until melted and glossy. Taste and season.
Add drained pasta to the sauce and toss over low heat 60 to 90 seconds, adding pasta water by the tablespoon if needed. Slice or shred chicken and return to the pan. Top with fresh basil and extra Parmesan. Serve immediately.
