I always mix the broth, bouillon, soy sauce, onion powder, mustard powder, and thyme together before I start cooking. Having this ready to pour saves you from fumbling with measuring spoons while the pan is hot. I also combine the flour and Parmesan for dredging on a plate nearby.
Slice each chicken breast in half lengthwise to make thinner pieces, then pound them to an even ½ inch thickness.
Dredge each piece in the flour and Parmesan mixture, tapping off the excess. Heat olive oil in a large skillet over medium-high heat and sear the chicken for 4-5 minutes per side until golden. Set the chicken aside on a plate.
Melt butter in the same skillet and scrape up the browned bits left behind, since that's where a lot of flavor lives. Add the whole garlic cloves and let them soften and turn golden for about 6-7 minutes over medium-low heat.
Sprinkle in the flour and stir constantly for 1-2 minutes until the raw flour smell disappears. This step is what thickens your gravy later, so don't rush past it. It should look like a thick, buttery paste at this point.
Pour in the broth mixture slowly in splashes, stirring the whole time to avoid lumps. Once combined, stir in the heavy cream and bring everything to a gentle boil before reducing the heat to a simmer.
Lower the heat and gradually stir in the Parmesan cheese until it melts smoothly into the sauce. Go slow here so the cheese doesn't clump or turn grainy. The sauce should look glossy and thick by now.
Return the seared chicken to the skillet along with any juices from the plate. Spoon the sauce generously over each piece, cover partially, and let everything simmer together for about 5 minutes.
While the sauce simmers, boil your cubed potatoes in salted water until fork-tender, about 15-18 minutes. Drain well, then mash with warm milk, butter, and salt until smooth and fluffy.
Spoon a generous portion of mashed potatoes onto each plate, then top with a piece of chicken and plenty of that garlicky sauce. Finish with a sprinkle of fresh parsley for color and a fresh, herby finish.