Heat the olive oil in a large heavy-bottomed pot (at least 5-6 quart capacity) over medium heat and melt the butter into it. Add the cubed chicken, season with salt and black pepper, and cook for 6-8 minutes until golden brown on all sides. Remove the chicken from the pot and set aside.

In the same pot (don't wash it - those brown bits add flavor), add the diced onion, carrots, celery, and fennel. Season with ½ teaspoon salt and cook for 8-10 minutes, stirring occasionally, until the vegetables soften and the onions become translucent but not browned.

Stir in the chopped garlic, rosemary, and thyme. Continue cooking for another minute until fragrant, being careful not to burn the garlic.

Pour in the chicken stock and turn up the heat to bring to a boil. Add the tortellini and cooked chicken back to the pot, then lower the heat to maintain a gentle simmer. Cook for 2-3 minutes for fresh refrigerated tortellini, 4-5 minutes for frozen tortellini, or 7-8 minutes for dried tortellini (or follow package directions).

Turn off the heat completely (this prevents the pesto from separating) and stir in the pesto, grated Parmesan, and fresh basil leaves. Taste and adjust seasoning with additional salt (you'll likely need ½ to 1 teaspoon more) and black pepper. Serve hot with extra Parmesan and fresh basil on top.