2Pat the chicken thighs dry and season generously with salt and pepper.
3Heat the olive oil in a large oven-safe skillet over medium-high heat. Add the chicken skin-side down and cook until golden and crispy. Flip and cook briefly, then remove from the pan and set aside.
4Reduce the heat to medium. Add the butter, onion, garlic cloves, and thyme to the same pan and cook, stirring occasionally, until the onion begins to soften and the garlic is lightly golden.
5Sprinkle in the flour and cook, stirring to coat everything.
6Slowly pour in the chicken broth, scraping up all the browned bits from the bottom of the pan. Bring to a gentle simmer, then reduce the heat to low and stir in the Asiago until melted and combined. Season with salt and pepper to taste.
7Add the baby potatoes and carrots and gently toss them in the gravy.
8Nestle the chicken thighs back into the pan skin-side up, keeping the skin above the sauce.
9Transfer to the oven and roast uncovered until the potatoes and carrots are tender and the chicken is cooked through to at least 165°F internally.
10Finish with fresh parsley and thyme, and spoon the gravy over everything.