Heat a large nonstick saucepan or cast iron Dutch oven over medium-high heat. Lightly coat with cooking spray. Add the ground turkey and cook, breaking up with a wooden spoon, until cooked through. Drain and discard the liquid. Transfer the ground turkey to a bowl.
Reduce the heat to medium and add the olive oil to the saucepan. Stir in the onion, carrot and celery. Cook until the vegetables are tender, about 5 minutes.
Stir in the garlic, thyme and pepper, and cook for 1 minute.
Add the pesto and chicken broth. Bring to a boil, reduce to a lively simmer and cook for 10 minutes.
Stir in the ground turkey and tortellini, and cook until the tortellini is tender, 5 minutes for fresh and 8 minutes for frozen.
Remove from the heat and stir in the parsley. Serve.