Preheat oven to 400°F (204°C). Line a large baking sheet with parchment paper. Spread the vegetables out in a single layer on the baking sheet. Drizzle with 1 Tablespoon olive oil, and stir to coat. Sprinkle with salt and pepper. Bake the vegetables for 20 minutes.

Heat the remaining 1 Tablespoon of olive oil in a large 12-inch skillet over medium heat, and swirl to coat. I usually use a cast iron skillet, but any skillet this size works. You can also use a Dutch oven. Place the chicken thighs in the skillet, sprinkle with salt and pepper, and cook for 4 minutes on each side. You want the chicken lightly browned on the outside, but not fully cooked in the centers because they will finish cooking in the oven. Transfer chicken to a plate and loosely cover with foil. You’ll add it back to the pan in step 4.

Add the butter to the hot pan (no need to wipe it out first), and gently swirl to coat as it melts. Add the salt, pepper, onion, garlic, parsley, and chicken broth. Cook and stir, scraping up any browned bits from the bottom of the skillet. Let the sauce simmer for 5 minutes, stirring/scraping occasionally. With a fork, whisk together the half-and-half and cornstarch. Slowly pour the half-and-half/cornstarch mixture into the skillet, stirring or whisking to combine. Cook, stirring, for 1 minute. Taste and adjust seasoning if needed.

Add the chicken and roasted vegetables to the skillet, stirring to coat everything in the sauce. Transfer the skillet to the oven and bake for 5–10 minutes, or until the chicken is cooked through (internal temperature should be at least 165°F (74°C)).

Remove from the oven and garnish with fresh parsley before serving, if desired.

Leftovers keep well in the refrigerator for a few days. You can reheat on the stove over medium heat or in the microwave.