In a small saucepan over medium-low heat, combine ½ cup of heavy cream with 3 minced garlic cloves. Stir occasionally for about 5 minutes until fragrant, then remove from heat and whisk in ⅓ cup of mayonnaise. Season with salt and pepper to taste, then set aside.

In a large mixing bowl, combine the remaining 3 minced garlic cloves, 1 lb of ground beef, 1 tsp of garlic powder, and a generous pinch of salt and pepper. Mix gently until just combined, then form into 4 patties.

Heat a skillet or grill pan over medium-high heat. Once hot, add the burger patties and cook for 4-5 minutes on one side. Flip carefully and grill for an additional 4-5 minutes until they reach an internal temperature of 160°F. Let patties rest for 2 minutes.

While the patties are resting, slice the brioche buns in half. Butter the cut sides with 2 tablespoons of melted butter and toast them in the same skillet or under a broiler for 1-2 minutes until golden brown.

To assemble, place fresh arugula on the bottom half of each bun, add a beef patty, drizzle with the garlic sauce, and top with the other half of the bun. Serve immediately.