Add two tablespoons of oil to a large oven-safe skillet and place on the stovetop over medium heat.
Season the chicken thighs with salt, pepper, and thyme on both sides.
Place the chicken thighs directly on the grill grates and cook for 15 minutes.
While the chicken cooks, prep your sauce by adding the olive oil and the butter to the pan. Add the minced garlic and red pepper flakes to the pan and sauté for 30-60 seconds.
Pour in the chicken broth, white wine, and sun-dried tomatoes. Bring to a simmer.
Reduce the heat of the grill to 350°F. Return the chicken to the pan, and place the whole skillet into your preheated pellet grill.
Let the chicken cook for about 30 minutes or so, or until the internal temperature reaches 165°F and the sauce has reduced a bit.
Remove from the grill and stir in the cream to the sauce.
Top with Parmigiano Reggiano and serve hot over mashed potatoes or buttered noodles.