Melt 2 tablespoons butter in a large pot over medium heat. Add mushrooms, onion, and garlic; increase heat to medium-high. Cook and stir until mushrooms are golden brown, 3 to 5 minutes.

Stir Marsala wine, chicken stock, brown sugar, lemon juice, molasses, and corn syrup into mushroom mixture; bring to a boil. Cook, stirring frequently, until liquid reduces by about half, 10 to 15 minutes.

Whisk cornstarch into cold water in a small bowl; slowly whisk into Marsala sauce, whisking continually. Cook and stir until sauce thickens, 10 to 15 minutes more.

Heat olive oil with remaining 1 tablespoon butter in a large skillet over medium heat; cook chicken until golden brown, no longer pink in the center, and the juices run clear, 3 to 5 minutes per side.