Preheat oven to 425°F with a rack in the lower third position. Generously coat a 6-cup jumbo muffin tray with cooking spray; set aside.
Toss together hash browns, cheese, cornstarch, cayenne, ½ teaspoon salt, and ¼ teaspoon black pepper in a large bowl until evenly distributed. Place 3 tablespoons of the hash brown mixture in each well and firmly press into bottom. Divide remaining hash brown mixture evenly among wells and press firmly up the sides.
Bake the hash browns until golden brown around edges, 25 to 30 minutes. Remove tray from oven, carefully crack eggs into each well, and sprinkle evenly with remaining ¼ teaspoon salt.
Bake the egg cups until whites are set and yolks are runny, 8 to 10 minutes. Let cool in tray for 5 minutes. Run a small offset spatula around edges to loosen. Carefully transfer egg cups to a platter, sprinkle with remaining ¼ teaspoon black pepper, and garnish with hot honey and chives.
