Mushrooms: Melt butter in cast iron skillet over medium heat. Stirring occasionally, sauté mushrooms and salt until all water has evaporated, about 15 minutes. Add garlic and stir until fragrant, about 1 minute. Set aside on plate.
Burgers: In a medium bowl mix together breadcrumbs, garlic, cumin, salt, and pepper. Add milk and mix until an even consistency. Let sit for 3-5 minutes. Sprinkle ground beef on breadcrumb mixture and combine with hands until evenly distributed. Form into 4-6 patties.
Melt butter in a cast iron skillet over medium heat. Cook burgers until internal temperature of 160 degrees F, about 8-10 minutes on each side. Add cheese and cook until melted.
Rolls: Preheat oven to 400 degrees F. Spray rolls lightly with oil and arrange in a single layer on a baking sheet. Toast in oven until warm and slightly brown, about 5 minutes.
Serve burgers on toasted rolls topped with sautéed mushrooms :-)