Put the bratwursts in a medium pot in a single layer.
Pour in the beer, then add enough water to cover the bratwursts by 1 inch, if necessary. Bring to a boil, then reduce the heat to medium low. Simmer until the bratwursts are cooked through, 12 to 14 minutes.
Remove to a plate and allow to cool completely.
Meanwhile, combine the ground beef, Worcestershire sauce, 1/2 teaspoon salt and a few grinds of pepper in a medium bowl. Gently mix with your hands and divide into 4 equal portions.
Lay out a piece of plastic wrap. Arrange 4 bacon slices side by side on the plastic to form a rectangle, overlapping them slightly. Position the bacon rectangle with a short end in front of you. Press a portion of the beef over the half of the bacon rectangle closest to you.
Place a bratwurst horizontally on top of the beef. Using the plastic wrap to help, tightly roll the bacon and beef around the bratwurst away from you; remove the plastic wrap. Secure the bacon with kitchen twine in 3 or 4 spots. Repeat to wrap the remaining bratwursts.
Place the bacon-wrapped bratwursts seam-side down in a large nonstick skillet over medium heat. Cook, turning, until the bacon is crisp and the beef is cooked through, about 10 minutes.
Remove to a plate, tent with foil and let rest 10 minutes.
Meanwhile, preheat the broiler.
Drizzle the insides of the buns with olive oil.
Place on a baking sheet and broil until golden brown, about 1 minute. Use scissors to remove the twine from the bratwursts.
Place on the buns and top with the chopped onion and cheese.
