Preheat your oven to 400°F (200°C) and line a small baking sheet with parchment paper.
Trim the woody ends off the asparagus and toss the spears with 0.5 tsp of olive oil, a pinch of sea salt, and black pepper.
Spread the asparagus on the baking sheet and roast for 8 minutes until they are just beginning to soften and turn vibrant green.
While the asparagus roasts, whisk together the Greek yogurt, lemon juice, garlic powder, and half of the chopped fresh dill in a small bowl.
Spread the yogurt mixture evenly into the bottom of a small oven-safe skillet or shallow baking dish.
Use the back of a spoon to create four shallow wells in the yogurt and carefully crack one egg into each well.
Remove the asparagus from the oven and arrange the spears around the eggs in the baking dish, then drizzle the remaining 0.5 tsp of olive oil over the eggs.
Place the dish in the oven and bake for 10-12 minutes, or until the egg whites are fully set and opaque while the yolks remain soft.
Remove from the oven and garnish with the remaining fresh dill and an extra crack of black pepper before serving immediately.