1. Preheat oven to 475 degrees. Coat 6 nonstick jumbo muffin cups with 1/2 teaspoon unsalted butter. In a large microwave-safe bowl, melt 4 teaspoons butter. Add 4 cups frozen hash browns (1 pound), thawed, and 2 egg whites; season with coarse salt and ground pepper and mix thoroughly. Place 1/2 cup mixture into each muffin cup, firmly pressing into bottom and up side of each cup. Bake 15 minutes. 2. Meanwhile, in a small nonstick skillet, melt 1/2 teaspoon butter over medium heat. Add 1 shallot, diced small; 1 small red bell pepper diced small; and 4 ounces ham steak, diced small. Cook, stirring occasionally, until shallot is softened, about 7 minutes. Season with salt and pepper. Divide vegetable mixture evenly among cups and top with 3 ounces cheddar, grated (3/4 cup). Bake 2 minutes. 3. Remove from oven and crack 1 large egg into each cup. Season with salt and pepper and bake until whites are set but yolks are still runny, about 8 minutes to 10 minutes. With a small offset spatula, remove cups from pan and serve immediately.