Begin by caramelizing the onion slices over low heat in a pot with the olive oil. Watch it carefully, stirring frequently for about 30 minutes, until the onions are soft and brown. In the meantime, cook and shred the chicken, prepare the tortellini according to package instructions, and prepare sauce.

To prepare the sauce, melt butter in a large pan and saute garlic for 3 minutes over medium heat. Add in cream and parmesan cheese and bring to a simmer. Reduce heat and simmer over medium low heat until thickened, about 15 minutes.

When the sauce is thick, stir in the pesto and allow it to cook about 5 more minutes. When the onions, chicken, and sauce are all prepared, toss them all gently together in one pan. Serve immediately.