Pit the cherries and then slice them into quarters. Add to a small saucepan. Measure and add the balsamic and dijon to the cherries.
Slice the onions and shallots.
Split the ground beef into four equal parts, make patties, and season both sides with kosher salt and pepper or your favorite burger seasoning. Set aside and let come to room temperature while you cook the cherries and onions.
Simmer the Cherries
Place the saucepan of cherries on medium heat and bring to a slight boil. Reduce to low and let simmer while you carmelize the onions, stirring occasionally.
Caramelize the Onions
Heat the olive oil in a cast iron skillet to medium-high. Add the onions, season with kosher salt and pepper, and cook until they start to release their moisture. Add the sprigs of thyme and rosemary and continue to cook at medium. When the pan becomes dry, add a small amount of water, stirring occasionally. Continue the process of adding water when dry and stirring until the onions are a deep golden brown color, about 15-20 minutes.
Make the Jam
When the onions are ready, remove the sprigs of rosemary and thyme, and then add the cherries to the pan and mix to combine. Reduce to low and let simmer while you grill the burgers. Once the burgers are done, remove from the heat and let cool for a bit.
Grill the Burgers
Heat your grill to medium-high and cook the burgers for approximately 4-5 minutes each side for medium. After you flip the burgers, add the buns and toast, watching carefully to not burn them.
Build your Burger
Spread mayo on both sides of the bun. Add some arugula to the bottom bun, add the burger, add the cherry onion jam, and the Roquefort. Add the top bun, and enjoy!