Step 1: Prepare the chicken. Season both sides of the chicken breasts generously with salt and pepper. Dredge the chicken in the ½ cup all-purpose flour, shaking off any excess. Set aside.
Step 2: Sear the chicken. Heat 2 Tablespoons of olive oil in a large skillet over medium-high heat. Add the floured chicken and sear for 3-4 minutes per side, until golden brown. Remove chicken from the skillet and set aside on a plate.
Step 3: Sauté mushrooms and garlic. Add the remaining 1-2 Tablespoons of olive oil and 2 Tablespoons of butter to the skillet. Add the sliced mushrooms and cook for 5-7 minutes, stirring occasionally, until they are tender and have released their liquid. Add the minced garlic and cook for 1 minute more until fragrant.
Step 4: Deglaze and build the sauce base. Pour in the dry white wine (if using) and deglaze the pan, scraping up any browned bits from the bottom. Let it simmer for 1-2 minutes until slightly reduced. Add the beef broth, chicken bouillon (or Better Than Bouillon), soy sauce, onion powder, mustard powder, and dried thyme. Bring to a gentle simmer.
Step 5: Thicken the sauce. In a small bowl, whisk together the 3 Tablespoons of cornstarch with 3 Tablespoons of cold water to create a slurry. Slowly whisk the cornstarch slurry into the simmering sauce. Continue to whisk gently until the sauce thickens to your desired consistency, about 2-3 minutes.
Step 6: Add cream and chicken. Reduce heat to low. Stir in the 1/3 cup heavy cream. Return the seared chicken to the skillet, nestling it into the sauce. Let it simmer gently for 5-7 minutes, or until the chicken is cooked through (internal temperature reaches 165°F / 74°C) and the sauce is heated through.
Step 7: Serve. Taste and adjust seasonings as needed. Serve hot over mashed potatoes, rice, or pasta, and enjoy!