In a small bowl, combine mayonnaise and hot sauce. Whisk until combined. Set aside.
Preheat Blackstone griddle to medium-high heat. Drizzle vegetable oil then add the sliced peppers and onions. Season with salt and pepper. Cook for 5-7 minutes until tender.
Smash the ground beef directly onto the griddle to make 4 smash burgers. Season with salt and pepper. Cook to desired doneness. Top with shredded pepper jack and cover until melted.
Remove burgers from the griddle. Toast sourdough on the griddle for 2 minutes per side. Remove from the griddle, top with mayonnaise, sautéed peppers and onions, sliced avocado and pickled carrots. Serve immediately.
