Pat the chicken pieces dry and season with 3/4 teaspoon of the salt, the pepper, and the Italian seasoning. Heat 1 tablespoon of the olive oil in the large skillet over medium-high heat until shimmering. Sear the chicken in a single layer, 3–4 minutes per side, until deeply golden — work in two batches if needed so it browns instead of steaming. Transfer to a plate; the chicken does not need to be fully cooked through yet.

Add the remaining 1 tablespoon olive oil to the same skillet. Add the zucchini and tomatoes in a single layer and cook undisturbed for 2 minutes, then stir and cook 2 minutes more until the zucchini is golden at the edges and the tomatoes are starting to slump. Season with the remaining 1/4 teaspoon salt.

Stir in the garlic and red pepper flakes; cook 30 seconds until fragrant. Pour in the chicken broth, scraping up every browned bit from the bottom of the pan with a wooden spoon. Let it simmer 1–2 minutes until slightly reduced. Those browned bits are the backbone of the sauce.

Reduce the heat to medium. Pour in the heavy cream and simmer gently 1–2 minutes, then sprinkle in the Parmesan a handful at a time, stirring until melted and silky.

Take the skillet OFF the heat. Stir in the basil pesto until the sauce is a uniform green, then fold in the spinach a handful at a time, stirring until just wilted. Adding the pesto off the heat keeps its bright basil flavor fresh instead of cooked down and dull.

Return the chicken (plus any juices from the plate) to the skillet. Simmer gently 2–3 minutes over low heat until the chicken is cooked through and the sauce coats a spoon. Shower with torn basil and extra red pepper flakes, and serve over rice, pasta, or with crusty bread.