Heat 1 tbsp. olive or avocado oil in a large cast iron or nonstick pan; season chicken breasts with 1 tsp. salt and sear until golden and cooked through, about 5 minutes per side. remove from pan.
Add zucchini and asparagus to the same pan; saute 2-3 minutes. add cherry tomatoes, garlic, remaining salt, pepper, oregano, and peas. stir to combine. pour in cream and broth; bring to a light boil and simmer for 5 minutes to thicken the sauce. stir in spinach and cook until wilted.
Add chicken back to the pan and top with grated parmesan or pecorino romano cheese, if desired.
