In a shallow pan or dish, mix together the flour and garlic salt. Season the chicken with salt and pepper, and then dredge the breasts in the flour mixture; set them aside.
Heat 2 tablespoons of butter in a large skillet over medium-high heat. When the butter is half melted, add a tablespoon of olive oil.
Transfer two of the chicken breasts to the skillet and cook them until they're golden brown—about 3-4 minutes per side. Transfer them to a paper towel-lined plate and repeat this step with the other two chicken breasts.
Add another tablespoon of butter to the pan, let it melt, and scrape up those pan bits—these will give the gravy a ton of extra flavor.
Add the mushrooms and shallots to the pan and sauté them until the mushrooms are tender—about 5 minutes. Then add the garlic and sauté for about a minute.
Pour the marsala wine into the pan, then add the balsamic vinegar, broth, and a dollop of that beef base; simmer until it's thickened and is reduced by about half, stirring occasionally. This should only take about 5 minutes.
Stir the cream into the sauce and pop the chicken back into the pan. Smother it with the sauce and simmer until the sauce has thickened a bit, about 3 minutes.
Garnish with fresh chopped parsley and serve!