Preheat and Season the Chicken: Preheat the oven to 400°F (200°C). Pat the chicken thighs dry with paper towels and season generously with salt, black pepper, chopped rosemary, and thyme.
Sear the Chicken: In a large, oven-safe skillet, heat the olive oil and 1 tablespoon of butter over medium-high heat. Add the chicken thighs, skin-side down, and cook for 4-5 minutes until the skin is golden brown and crispy. Turn the chicken over and continue cooking for an additional 3 minutes on the opposite side.
Add Garlic and Roast: Add the peeled garlic cloves to the skillet, scattering them around the chicken. Pour in 1 cup of chicken broth. Transfer the skillet to the preheated oven and roast for 25-30 minutes, or until the chicken is fully cooked and the garlic is tender.
Prepare the Asiago Gravy: While the chicken is roasting, start the gravy. In a medium saucepan, melt 2 tablespoons of butter over medium heat. Gradually whisk in the flour and cook for 1 to 2 minutes, stirring constantly to form a roux. Gradually add the chicken broth, whisking continuously to prevent lumps, then add the heavy cream. Bring the mixture to a gentle simmer and cook for 3-5 minutes until slightly thickened.
Add Asiago and Season: Stir in the grated Asiago cheese until melted and smooth. Adjust the flavor of the gravy by seasoning it with salt and freshly cracked black pepper to your liking. Keep the gravy warm over low heat until the chicken is ready.
Serve: Remove the chicken from the oven and spoon some of the roasted garlic and pan juices over each thigh. Plate the chicken and drizzle with the Asiago gravy.