Bring a large pot of salted water to a boil. Add the cheese tortellini and cook according to package instructions, typically about 3 to 5 minutes until they float to the surface. Once done, drain and set aside. Reserve about 1/4 cup of pasta water to loosen the sauce later if needed.
Heat the olive oil in a large skillet over medium-high heat. Add the peeled and deveined shrimp in a single layer. Season with salt, pepper, and half of the Italian seasoning. Cook for 2 minutes on one side until pink and slightly opaque, then flip and cook the other side for another 1 to 2 minutes. Remove shrimp from the skillet and set aside.
Lower the heat to medium and add the minced garlic to the skillet. Sauté for about 30 seconds until fragrant, being careful not to burn it. Pour in the chicken broth and heavy cream, stirring to combine. Let the sauce simmer gently for 3 to 4 minutes until slightly thickened.
Stir in the grated Parmesan cheese and the remaining Italian seasoning. Continue stirring until the cheese melts and the sauce becomes smooth and creamy. If the sauce feels too thick, add a splash of the reserved pasta water to reach your desired consistency.
Return the cooked shrimp to the skillet, then add the drained tortellini. Toss everything gently to coat the pasta and shrimp evenly with the creamy garlic sauce. Cook together for another minute to warm through and allow flavors to meld.
Remove from heat and sprinkle with freshly chopped parsley for a pop of color and freshness. Serve immediately while warm.