Preheat the oven to 350°F.
Heat 1 tablespoon olive oil in a medium cast-iron grill pan over medium-high heat. Add the onions to the pan, season with salt and pepper, and cook on both sides, until the onions are slightly soft, approximately 7-8 minutes total. Remove from the heat and set aside.
In a medium bowl, whisk the eggs until combined. Add the green garlic, half of the dill, lemon juice, cheese, and season with salt and pepper. Stir until combined.
Heat the remaining 3 tablespoons olive oil in a medium cast-iron skillet over medium-high heat. Add the egg mixture to the skillet. Cook for 5 minutes. Arrange the spring onions, cut side up, over the top. Sprinkle with the remaining dill. Remove from the heat.
Place the skillet in the oven and bake for 20 to 25 minutes. Remove from the oven. Slice into wedges. Serve immediately.