Place your cast-iron skillet over medium-high heat on your stove, or crank up your grill to medium-high heat.
If using your cast-iron skillet, add 1 tablespoon of canola oil.
Once fully heated, add the patties. Cook on one side for about 4 minutes. Then flip.
Cook on the other side for about 4 minutes.
In the last minute, add the cheese.
Place a large pot over the burgers to melt the cheese evenly.
Meanwhile, slice the buns, butter them, and place under the broiler for about 3 minutes (keep an eye on them! Time varies depending on oven).
Remove burgers from heat source.
Add rosemary aioli
to bottom bun.
Place the burger on the bottom bun.
Generously add caramelized onions on top of the burger.
Place toasted bun on top.