Prepare Asparagus: Begin by trimming the ends of your asparagus and using a vegetable peeler to shave thin, delicate layers. Layer these shaved asparagus strips evenly in two medium, flat ramekins for a lovely presentation.

Make Cream Mixture: In a small bowl, whisk together the heavy cream, Dijon mustard, kosher salt, black pepper, and freshly chopped dill until smooth. Pour half of this luscious cream mixture over the asparagus layers in the ramekins.

Add Eggs: Gently create small wells in the asparagus mixture with your fingers or a spoon. Carefully crack a large egg into each well, then drizzle the remaining cream mixture over the egg whites, taking care not to cover the yolks.

Bake: Place the ramekins in a preheated oven set to 375°F. Bake for about 12-15 minutes, or until the egg whites are fully set and the yolks reach your desired level of doneness.

Finish and Serve: Once perfectly baked, finish your dish by topping the shirred eggs with extra dill, a pinch of red pepper flakes, and a sprinkle of flaky sea salt. Serve immediately.