Combine chicken broth, bouillon cube, soy sauce, onion powder, mustard powder, and thyme in a large measuring cup with a spout. Set aside. Mix flour and shredded Parmesan cheese together on a flat plate.

Slice each chicken breast in half lengthwise to create 2-3 thinner cutlets. Cover with plastic wrap and pound to 1/2 inch thick using the textured side of a meat mallet. Pat completely dry with paper towels.

Season each cutlet with Italian seasoning, salt, and pepper. Dredge in the flour and Parmesan mixture, tapping off any excess.

Heat olive oil in a large skillet over medium-high heat. Sear the chicken in batches for 4-5 minutes per side until deep golden brown. Set aside on a plate.

Reduce heat to medium-low and melt butter in the same skillet. Use a silicone spatula to scrape up all the browned bits from the bottom. Add the whole peeled garlic cloves and cook for 6-7 minutes, stirring occasionally, until lightly golden and fragrant.

Sprinkle in the flour and stir for 1-2 minutes until the raw flour smell disappears. Add the broth mixture in slow splashes, stirring continuously to keep the sauce smooth.

Stir in the heavy cream. Bring to a gentle boil, then reduce heat to low. Gradually stir in the Parmesan cheese until melted and silky.

Nestle the chicken back into the skillet along with any juices from the plate. Spoon the sauce generously over the top. Cover partially and simmer for 5 minutes. Garnish with fresh parsley and serve warm.