Pat chicken pieces dry with paper towels and season generously with salt and black pepper on both sides. Heat 3 tablespoons olive oil in a large skillet over medium-high heat until shimmering, about 90 seconds. Working in batches to avoid crowding, sear chicken for 3-4 minutes per side until golden brown, then transfer to a plate. Don't worry if it's not fully cooked—it will finish in the sauce.
Reduce heat to medium and add diced onion to the same skillet, scraping up browned bits with a wooden spoon. Cook for 2-3 minutes until onion softens and becomes translucent. Add minced garlic and cook for another 30 seconds until fragrant but not browned—this prevents bitterness.
Stir in tomato paste and cook for 1-2 minutes, allowing it to caramelize slightly and deepen in color. Pour in chicken broth to deglaze the pan, scraping the bottom with your spoon to release all the flavorful bits stuck there.
Return chicken pieces to the skillet and add sun-dried tomatoes and Italian seasoning. Bring the mixture to a gentle simmer, then reduce heat to medium-low and cook covered for 8-10 minutes until chicken is nearly cooked through and the sauce begins to reduce slightly. The chicken reaches 165°F internal temperature at this point.
Stir in heavy cream and butter, combining gently until the sauce becomes velvety and coats the back of a spoon. Add fresh spinach in handfuls, stirring until it wilts completely into the creamy sauce—this happens in about 2 minutes and adds nutritional depth without changing flavor.
Remove from heat and fold in fresh basil and grated Parmesan cheese, reserving a small handful of basil for garnish. Taste and adjust seasoning with salt and pepper as needed, keeping in mind that Parmesan adds saltiness. Serve immediately over pasta, rice, or crusty bread to catch every drop of that elegant sauce.