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Preheat oven to 350 degrees F (175 degrees C). Grease a large 6-cup muffin tin with cooking spray. Mix potatoes, melted butter, salt, and pepper together in a large bowl. Divide potato mixture among muffin cups. Press to create a thin crust over the bottom and up the sides of each cup. Bake in the preheated oven until edges are a light golden brown and potatoes are tender, about 30 minutes. Crack an egg gently into each cup. Continue cooking until egg whites are set and yolk is runny, about 6 minutes. Remove from the oven; cover eggs with provolone cheese. Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Toss prosciutto with maple syrup and pepper in a small bowl. Spread out on a small baking sheet lined with aluminum foil. Place muffin tin and baking sheet under the preheated broiler. Broil until cheese is melted and prosciutto is crisp, about 1 minute. Transfer egg baskets to a serving plate. Chop prosciutto and sprinkle on top.