Cook the pasta according to package directions in well-salted water until al dente. Reserve about 1/2 cup of pasta water before draining, in case you need to thin the sauce later.
While pasta cooks, season chicken pieces generously with salt and pepper. Heat 1 tablespoon olive oil in a large skillet over medium-high heat until shimmering.
Add the chicken to the hot skillet in a single layer without overcrowding. Cook for 5-6 minutes, turning occasionally, until golden brown on all sides and cooked through (internal temperature of 165°F). Remove to a plate and set aside.
Reduce heat to medium and add remaining tablespoon of olive oil to the same skillet. Add minced garlic and cook for 30 seconds until fragrant, being careful not to burn it.
Stir in the sun-dried tomatoes and cook for 1 minute to release their flavors into the oil.
Pour in the heavy cream and chicken broth, scraping the bottom of the pan to loosen any flavorful browned bits. Bring to a gentle simmer.
Add the Parmesan cheese, Italian seasoning, and red pepper flakes if using. Stir until the cheese is melted and sauce is smooth, about 2 minutes.
Return the cooked chicken to the skillet and add the chopped spinach. Stir until spinach is wilted, about 1-2 minutes.
Add the drained pasta directly to the sauce and toss everything together until well coated. If the sauce seems too thick, add a splash of the reserved pasta water to loosen it.
Taste and adjust seasonings with salt and pepper. Garnish with fresh herbs if desired and serve immediately while hot.