French Onion Burgers
In a heavy-bottomed stock pot or skillet set over medium heat, melt the butter then stir in the onions, garlic and a pinch of kosher salt. Cook the onions, stirring frequently, for 15 minutes. Add the bouillon mixture and continue cooking the onions until they are dark golden and caramelized, an additional 15 to 20 minutes. Remove the caramelized onions from the pan and set them aside.
Season the burger patties with kosher salt and black pepper.
Set your gas grill to medium-high heat or place a grill pan over medium-high heat on the stove top. Allow the grill to heat up for several minutes. If using a gas grill, oil the grates.
Place the burgers on the grill and cook, flipping once, until they reach your desired level of doneness. (For medium-rare burgers, cook 5 to 7 minutes total.) Just prior to removing the burgers, top with the cheese and cover until the cheese is melted, about 1 minute.
Remove the burgers from the grill.
In a medium bowl, toss the arugula with the olive oil and a pinch of kosher salt and pepper.
Place the burger on the bottom bun, top with the caramelized onions and dressed arugula then serve.