Boil Potatoes: Place cubed potatoes in a large pot of cold, salted water. Bring to a boil and cook for 12-15 minutes until fork-tender. Drain well. Return to the warm pot for 1 minute to evaporate excess moisture. Mash with warm butter, warm cream, sour cream, salt, and pepper until fluffy. Cover to keep warm while you prepare the rest of the chicken and mashed potatoes.
Prep Chicken: Slice chicken breasts horizontally into 4 cutlets. Pound to an even 1/2-inch thickness. Pat completely dry. Season both sides with salt, pepper, garlic powder, onion powder, and paprika. Lightly dredge the cutlets in 1 tbsp of flour, shaking off any excess.
Sear Chicken: Heat olive oil and 1 tbsp of butter in a large skillet over medium-high heat. Sear chicken for 4-5 minutes per side until golden brown and internal temperature reaches 165°F. Remove to a plate and cover loosely with foil.
Caramelize Garlic: Reduce heat to medium-low. Add remaining 2 tbsp of butter and whole garlic cloves to the skillet. Cook for 3-4 minutes until garlic is fragrant and lightly golden.
Make the Roux: Sprinkle flour over the butter and garlic. Whisk constantly for 1-2 minutes.
Build Gravy: Slowly whisk in the chicken broth and beef bouillon, scraping up all the brown bits from the bottom of the pan. Stir in the heavy cream. Bring to a gentle simmer and let thicken for 3 minutes.
Finish: Reduce heat to low. Whisk in Parmesan cheese until melted. Return the chicken and any resting juices from the plate back into the skillet. Simmer for 2 minutes to heat through.
Serve: Spoon the creamy garlic gravy generously over the chicken and hot mashed potatoes. Garnish with fresh parsley and serve your perfect chicken and mashed potatoes immediately.