Bring a large pot of salted water to a boil and cook the cheese tortellini according to the package directions. Reserve ½ cup of pasta water, then drain.
Season the shrimp with salt, pepper, and Italian seasoning.
Heat olive oil and butter in a large skillet over medium-high heat.
Cook the shrimp for 1–2 minutes per side until pink. Remove them from the skillet and set aside.
Reduce the heat to medium and add the minced garlic. Cook for about 30 seconds until fragrant.
Pour in the chicken broth and heavy cream, stirring to combine.
Add the Parmesan cheese and stir until melted and smooth.
Mix in the basil pesto until fully incorporated.
Add the spinach, if using, and cook until just wilted.
Return the shrimp and cooked tortellini to the skillet, gently tossing to coat everything in the sauce.
Add a splash of reserved pasta water if the sauce needs thinning.
Garnish with fresh basil and extra Parmesan before serving.