Preheat the oven to 180°C degrees.
Squeeze most of the water out of the spinach, but these should not be crushed—a little water is still fine.
Heat a large ovenproof skillet over medium-high heat. When hot, add 1 tsp olive oil, then add the onion and 1/2 tsp salt and cook until soft and transparent - 3 to 5 minutes.
Add the shallots and cook them, stirring constantly, until they just soften - about 1 minute.
Add the spinach, dill, 1/2 cup feta, lemon juice, remaining 1/2 tsp salt and pepper and mix until well combined and heated. Remove from heat.
Make four wells on top, crack one egg each and season each with a little salt and pepper.
Top spinach with remaining 1/4 cup feta.
Carefully place the pan on the middle rack and wait until the egg whites are 8 to 13 minutes to your liking.