Cook the pasta. Boil in well-salted water until just shy of al dente. Reserve 1 cup of pasta water, then drain.
Season the chicken. Pat dry and season with 1 teaspoon salt, 1/2 teaspoon black pepper, and half the Italian seasoning.
Sear the chicken. Heat 1 tablespoon olive oil in a large skillet over medium-high. Add chicken in a single layer.
Sear 3–4 minutes per side until golden and just cooked through. Transfer to a plate.
Sauté aromatics. Lower heat to medium. Add remaining 1 tablespoon olive oil, garlic, and sun-dried tomatoes.
Cook 1 minute until fragrant. Stir in tomato paste and cook another minute to caramelize.
Build the sauce. Pour in chicken broth and milk, scraping up browned bits. Stir in remaining Italian seasoning and red pepper flakes.
Simmer 3–4 minutes to slightly reduce.
Make it creamy. Lower the heat to low. Whisk Greek yogurt in a small bowl with a few spoonfuls of hot sauce to temper, then whisk it into the pan. Add Parmesan and stir until smooth.
Finish the pasta in the sauce. Add drained pasta and cooked chicken to the skillet.
Toss, adding splashes of reserved pasta water as needed until the sauce is glossy and clings to the pasta.
Brighten and season. Stir in chopped basil and a squeeze of lemon juice with a pinch of zest. Taste and adjust salt, pepper, and heat.
Serve. Top with extra basil and a light dusting of Parmesan. Serve hot.