Preheat oven to 400°F (200°C).

Season chicken thighs on both sides with salt and pepper.

In a large skillet, heat 1 tablespoon butter and 1 tablespoon olive oil over medium-high heat. Brown chicken thighs, skin-side down first, for about 3 minutes per side, then transfer them to a baking sheet.

Bake the chicken for approximately 20 minutes, or until fully cooked, then set aside.

Drain excess fat from the skillet, leaving a small amount. Sauté minced shallots for 3-5 minutes until softened. Add sliced mushrooms and thyme leaves, continuing to sauté for another 5 minutes until tender. Pour in Marsala wine and bring to a simmer, then remove shallots and mushrooms to a plate.

Melt the remaining butter in the skillet, stir in Wondra flour, and cook for 1 minute while stirring constantly to create a roux. Whisk in chicken or beef broth/stock, then heavy cream, and stir until the mixture comes to a simmer and thickens. Taste and adjust seasonings as needed.

Return the mushrooms and wild rice to the skillet with the sauce and bring everything to a simmer. Nestle the cooked chicken thighs into the sauce and heat until the chicken is warmed through. Serve garnished with more fresh thyme.