Preheat oven to 350 degrees F (175 degrees C).

Place mushrooms in a food processor; pulse until finely chopped. Transfer to a roasting pan. Drizzle 2 tablespoons olive oil on top and mix. Sprinkle with salt.

Bake in the preheated oven until tender, about 10 minutes. Cool to room temperature, about 15 minutes.

Heat remaining 1 tablespoon olive oil in a large skillet over medium heat. Add kale; cook and stir until just wilted, 2 to 4 minutes. Let cool slightly, about 5 minutes.

Transfer kale to the food processor; pulse until finely chopped.

Combine mushrooms, kale, Italian sausage, and harissa in a bowl; mix together by hand. Form into 4 patties, taking care not to pack them too firmly.

Heat an oven-safe grill pan or cast iron skillet over medium-high heat. Add patties; cook until browned, about 5 minutes. Flip.

Transfer grill pan to the oven and continue cooking until second side is browned, about 8 minutes. Place a slice of mozzarella cheese on top of each patty and broil until cheese melts, about 1 minute.

Serve patties on toasted buns with marinara sauce.