In a microwave-safe dish, combine potatoes and 1/3 cup water. Microwave on high for 6-7 minutes, or until potatoes are cooked. Set aside after draining.
Cut the chicken breasts in half through the equator to make four fillets. Wrap in plastic wrap and pound to a consistent thickness. Allow to air dry.
In a small bowl, combine the flour and all of the chicken spice. Dredge each breast in the mixture, shaking off any excess, and setting it aside on a dry surface.
In a large pan over medium-high heat, melt 2 tablespoons butter and 2 tablespoons oil.
When the pan is heated, add the chicken and cook for 4-5 minutes on each side (depending on thickness), or until golden and cooked through. Remove the chicken to a platter, but do not clean the skillet.
Over medium heat, combine 2 tablespoons butter and 1 tablespoon olive oil. Turn the heat up to medium-high and add half of the mushrooms. Stir to coat evenly in the butter, then place mushrooms in an equal layer.
Cook for 3 minutes per side, or until golden. When the mushrooms are properly browned, season them with freshly cracked salt and pepper and give them a good toss.
Remove the mushrooms from the skillet and repeat with the remaining mushrooms; place all of the mushrooms on a platter.
Reduce the heat to medium and add enough oil to equal about 1 1/2 teaspoons. Combine the potatoes, shallots, garlic, and red pepper flakes in a mixing bowl.
Cook for 2 minutes, or until shallots are softened. Reduce the heat to low and add the heavy cream. Add the chicken broth, cornstarch, balsamic vinegar, and all of the sauce ingredients to the skillet.
Bring sauce to a simmer, scraping off any brown pieces on the bottom of the pan, and continue to cook until sauce thickens to desired consistency, stirring often (not too thick).
Whisk in the Parmesan until melted, then push the potatoes to the side of the pan.
Stir in the mushrooms, then add the chicken to heat through and soak up the sauce. If desired, garnish with fresh parsley.