In a small saucepan, combine the heavy cream and 3 minced garlic cloves over medium-low heat. Stir gently and cook for about 5 minutes. Remove from heat and whisk in mayonnaise until smooth. Season with salt and pepper, then set aside.

In a mixing bowl, combine ground beef, remaining 3 minced garlic cloves, garlic powder, salt, and pepper. Mix gently and form into 4 patties.

Preheat a skillet over medium-high heat. Cook the patties for 4-5 minutes on each side until golden-brown. Let rest for 2 minutes.

Slice the brioche buns in half and butter the cut sides. Toast the buns in the skillet for 1-2 minutes until golden brown.

Assemble the burgers with arugula, beef patty, and creamy garlic sauce. Place the top bun on and serve immediately.