3 tablespoons olive oil, plus more as needed
1 ¼ pounds Yukon Gold or red new potatoes, scrubbed and diced into 1/2-inch pieces
Kosher salt and black pepper
½ large fennel bulb, diced into 1/2-inch pieces (about 1 cup), fennel fronds reserved
1 leek, trimmed, halved lengthwise and sliced 1/4-inch thick (about 1 cup chopped leeks)
½ pound asparagus (10 to 12 spears), trimmed and cut into 1/2-inch pieces
1 tablespoon fresh lemon juice, plus lemon zest and more juice for serving (optional)
4 large eggs
3 tablespoons crumbled plain goat cheese
1 tablespoon chopped fresh dill, mint or parsley
Heat the oven to 400 degrees. In a large (12-inch) ovenproof skillet, heat the olive oil over medium-high. Add the potatoes, spreading them out into an even layer, and season with 1/2 teaspoon salt and a few grinds of black pepper. Cook, tossing occasionally and scraping the bottom of the pan, until potatoes are nicely browned, 7 to 9 minutes.
Lower the heat to medium, add the fennel and leek, and cook, tossing occasionally, until leeks are translucent, 3 to 5 minutes. If the skillet looks dry at any point, add a splash of olive oil.
Add the asparagus, along with 1/2 teaspoon salt and a few more grinds of black pepper. Cook, tossing occasionally, until the asparagus, fennel and potatoes are tender, about 5 minutes.
Off the heat, add the lemon juice and toss, scraping up any brown bits from the bottom of the pan.
Use a spoon to create 4 small hollows in the hash. Carefully crack an egg into each, season the eggs with salt and pepper and bake for 5 to 7 minutes, until the egg whites are just set. (Don’t overcook.)
Sprinkle with goat cheese, herbs, fennel fronds and lemon zest, if using. Sprinkle with additional lemon juice, if desired, and a pinch of salt, and serve hot. (A spatula works best for serving.)