Melt butter in a heavy skillet over medium heat. Cook garlic in hot butter until browned, about 5 minutes.
Mash the garlic in the skillet and stir into the butter; add green bell pepper and onion and cook until the onion is translucent, 5 to 7 minutes.
Stir mushrooms into the pepper and onion mixture; cook and stir until the mushrooms are slightly browned, about 5 minutes. Stream heavy cream into the mixture while stirring; add Romano cheese and Parmesan cheese. Continue cooking until the mixture is hot and the cheese is melted, 5 to 10 minutes more.
Pour wine into the skillet and cook until the liquid is reduced in volume by half, 5 to 10 minutes; add chicken broth, bring to a simmer, and cook until slightly reduced, about 5 minutes.
Mix water and cornstarch together in a small bowl until cornstarch is completely dissolved; stir into the liquid in the skillet and cook, stirring regularly, until the liquid is thickened, 5 to 10 minutes.