Bring a large pot of salted water to a boil. Add the tortellini and cook according to package instructions, usually about 3-5 minutes. In the last 2 minutes of cooking, add the broccoli florets to the pot. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and red pepper flakes (if using) and sauté for about 1-2 minutes until fragrant, being careful not to burn the garlic.
Add the drained tortellini and broccoli to the skillet. Toss to coat in the garlic oil.
Sprinkle the grated Parmesan cheese over the tortellini and broccoli, stirring gently to combine. Season with salt, pepper, and lemon juice.
Cook for an additional 1-2 minutes until everything is heated through and the cheese is melted.
Serve hot, garnished with fresh parsley.