In a small glass bowl, soak the toothpicks in water for an hour. This helps them not burn while they're on the grill.
Cut the cheddar cheese into ¼-inch wide strips and set aside.
Slice the brats down the length of them and cut in about ¾ of the way, leaving the bottom casing intact. Stuff one piece of the cheese in the brat lengthwise. Pinch the opening of the brat over the piece of cheese as best as you can.
Tightly and carefully wrap two pieces of bacon around the length of the brat and secure it at both ends with a toothpick. Evenly wrap the brat in the bacon, this will help the cheese stay inside.
Stir the bbq sauce and the beer together in a small bowl and set it aside.
Remove the onion skin and root and slice the onion about 1/4th of an inch thick into rounds. In a medium-sized bowl, separate the onion layers. Toss them with olive oil, salt, and pepper.
Prep your grill over medium heat. Once it's hot, turn it down to medium-low heat.
Place the stuffed and wrapped brats directly onto the grates, cut side up and grill for about 5 minutes, start rotating the brats until the bacon cooks on the outside and an internal temperature reaches 160°F. Some of the cheese might leak out, but that is okay and should be expected.
Baste the brats with bbq sauce all over and continue to cook for about another 5 minutes, or until caramelized. Flip the brats around during this time so the bbq sauce doesn’t burn.
Once they are browned nicely and reach an internal temperature of 165°F, they are done, about 20 minutes total time on the grill.
While the brats are grilling, that's when you cook the onions. I like to make a little foil tray to put the onions in and stir them around every couple of minutes to prevent burning, they are ready when they are soft and lightly browned, they will be done around the same time as the brats.
When ready to serve the brats, place one into a hot dog bun, top with some of the onions, and serve immediately.