Preheat oven to 375 degrees. Butter 9-1/2" oval gratin pan.
Melt 1 T. butter in heavy medium skillet over medium heat. Add onion and cook until beginning to soften, about 5 minutes. Add asparagus, salt and pepper. Cook until asparagus begins to soften, about 4 minutes. Add bacon and stir 1 minute. Add 1/3 cup cream and pinch of cayenne pepper. Stir until heated through, 1 minute. Mix in mustard. Transfer to prepared pan.
Make 4 nests in mixture, spacing evenly. Break egg into each nest. Drizzle 1 t. cream over each egg. Sprinkle with salt, pepper, and cayenne. Bake until whites are beginning to set but are still runny, 12 minutes.
Preheat broiler. Sprinkle cheese over dish. Immediately broil until melted and beginning to brown, about 30 seconds. Serve immediately.