Add the liquid and quinoa to a medium sauce pan. Add the bay leave. Cook over medium heat, bringing it to a simmer. Stir occasionally. Let cook for 20 minutes or until the liquid is absorbed.
While the quinoa is cooking, heat the a large skillet with the oil and butter over medium to medium high heat. While the butter is melting, season both sides of the chicken with Italian seasoning and salt and pepper. Place the chicken into the hot skillet and let cook for 4 to 5 minutes. Flip and cook an additional 4 to 5 minutes on the other side. After flipping, season the asparagus with salt and pepper and add the asparagus to the pan, around the chicken. Make sure to periodically flip the asparagus. Add the 3 pressed garlic cloves, lemon juice, rosemary, and white wine. Bring the liquid to a slow simmer and let simmer for 3-4 minutes, and finish by stirring in half a cup of grated Parmesan cheese. Serve the chicken over the quinoa.