In a small saucepan combine the wine, shallots, garlic, and brown sugar. Bring to a boil over medium high heat.
Continue boiling for 20 minutes or until the mixture has reduced to a half cup, stirring occasionally.
Remove from heat and whisk in the butter until smooth. Season with salt and pepper.
In a medium bowl combine the ground beef, Worcestershire sauce, breadcrumbs, and half of the wine sauce. Mix well.
Divide the burger mixture into 4 burgers.
Heat a grill to medium high heat.
Cook the burgers for 3-4 minutes then flip them over, brush with the remaining wine sauce, and cook for 4-5 minutes or until the reach 125 degrees.
Place the cheese on top of the burgers and cook for an additional minute.
Place the burgers on a bun and top with lettuce.