1. Cook the tortellini: Bring a large pot of salted water to a rolling boil. Add the refrigerated cheese tortellini and cook according to package directions, usually 2-3 minutes, until they float to the surface and are tender. Drain the tortellini well and set aside. Do not overcook, as they will continue to soften slightly in the sauce.

2. Saute the aromatics: While the tortellini cooks, heat the olive oil in a large skillet or Dutch oven over medium heat. Add the chopped yellow onion and cook for 3-5 minutes, stirring occasionally, until it softens and becomes translucent.

3. Add the garlic: Stir in the minced garlic and cook for another minute until fragrant. Be careful not to burn the garlic, as it can turn bitter quickly.

4. Build the creamy base: Pour in the chicken or vegetable broth and bring it to a gentle simmer, scraping up any browned bits from the bottom of the pan. Reduce the heat to low, then slowly stir in the heavy cream. Let it warm through for about 1-2 minutes.

5. Incorporate the pesto and cheese: Remove the skillet from the heat. Stir in the prepared basil pesto until it is fully combined and the sauce is a uniform green color. Then, add the 1/4 cup of grated Parmesan cheese, stirring until it melts into the sauce and thickens it slightly.

6. Combine with tortellini: Add the drained tortellini to the skillet with the creamy pesto sauce. Gently toss everything together until the tortellini is thoroughly coated.

7. Season and serve: Taste the dish and season with salt and black pepper as needed. Remember that pesto and Parmesan can be salty, so add more salt cautiously. Serve immediately, garnished with extra grated Parmesan cheese and fresh basil leaves, if desired.