Preheat oven to 400 degrees F. Line a baking sheet with parchment paper.
Season parmesan with black pepper. Place spoonfuls of the parmesan onto the lined baking sheet and spread the cheese into flat discs. Bake the parmesan crisps for 3-4 minutes or until golden brown. Remove from the oven and let cool completely.
Fill a large deep pan with water. Bring to a boil over high heat and season the water with a pinch of salt. Add green beans to the pot and cook for 4-5 minutes. The green beans should still be crisp. Drain the water and run the green beans under ice-cold water.
Return the same pan to the stove and heat over medium heat. Melt 2 tablespoons butter in the pan and add sliced shallots. Season with salt, stirring to combine. Continue to saute until caramelized, about 20 minutes. If the pan gets too dry, add about 1-2 tablespoons of water.
Melt the remaining tablespoon of butter and add crushed garlic. Saute until golden brown. Add back green beans to the pan along with capers, mustard, lemon zest, and sumac. Season the green beans, tossing to coat with all of the ingredients. Saute for another 2 minutes or until the green beans are hot.
Remove from heat and transfer green beans to a serving platter. Break the parmesan crisps into small pieces and sprinkle on top. Sprinkle extra sumac and serve immediately.