Bring a large pot of salted water to a boil. Add tortellini and cook according to package directions. In the last 2 minutes, add broccoli florets. Drain well and set aside.

Heat olive oil in a large skillet over medium heat. Add garlic and sauté until fragrant, about 30 seconds, taking care not to burn.

Stir in diced chicken and cook for 1–2 minutes to warm through. Pour in heavy cream, stirring until it thickens slightly.

Reduce heat and mix in Parmesan until the sauce is smooth and creamy. If too thick, add a splash of pasta water.

Toss tortellini and broccoli into the skillet, coating well with the sauce. Season with salt and pepper.

Transfer to bowls, sprinkle with parsley, and serve warm.