Heat 1 tablespoon olive oil in a large skillet over medium‑high heat.
Add the cubed chicken, season with salt and pepper, and cook 4–5 minutes, stirring occasionally, until browned and cooked through; transfer to a plate and set aside.
Reduce heat to medium and add 2 tablespoons butter to the pan; once melted, whisk in 2 tablespoons flour and cook 1 minute to form a roux.
Slowly whisk in 2½ cups chicken broth and cook 2 minutes until the sauce begins to thicken.
Add the refrigerated tortellini and bring the mixture to a boil; cook about 4 minutes, stirring occasionally so the tortellini is evenly coated and heated through.
Stir in ½ cup heavy cream and ¼ cup grated Parmesan and cook 1 minute more until the sauce is creamy.
Return the cooked chicken to the pan and add 1½ cups fresh spinach; cook 2–3 minutes until the spinach wilts.
Fold in 1 cup halved cherry tomatoes, adjust seasoning with salt and pepper if needed, sprinkle with chopped parsley, and serve.