In a small skillet over medium heat, add the beer, pressed garlic and cheddar cheese. Cook, stirring frequently, until the cheese is melted. Remove from heat and pour into a freezer safe dish lined with wax paper. Freeze for one hour or until frozen.
While the cheese is freezing, mix together all the ingredients for the burgers together in a bowl until thoroughly combined. Set aside.
Heat olive oil in a griddle or skillet over medium heat.
Remove cheese from freezer and lift the wax paper out of the dish. Peel the wax paper off the frozen sheet of cheese. Cut the cheese into 9 squares. You will have some left over.
Divide the burger meat into 4 sections. Take one section of burger meat and wrap it around a cheese square, forming a thick burger. Repeat with other sections.
Sear the burgers for 2-3 minutes prior to flipping and searing on the other side. Finish off over indirect heat on a grill or in a 350 degree oven for 10 minutes or until burgers reach desired doneness.
Put burger on a bun, top with more cheese and red onion if desired. Enjoy.
Notes
You will have left over beer cheese. You could double up on the stuffing in the burger for super cheesy stuffed burgers.