Preheat the oven to 375°F. Heat the olive oil in a large oven-safe skillet over medium heat. Add the shallot and garlic and cook for 1-2 minutes until fragrant.
Add the spinach in batches, tossing until wilted, about 3-4 minutes total. Stir in the nutmeg, salt, and pepper, then cook off any excess liquid, about 2 minutes more.
Using a spoon, push the spinach into 4 shallow nests around the skillet, leaving a well in the center of each.
Crack one egg into each spinach nest. Season the eggs with a pinch of salt and pepper.
Transfer the skillet to the oven and bake for 8-10 minutes, until the egg whites are set but the yolks are still soft, baking a few minutes longer for firmer yolks.
Garnish with fresh chives and red pepper flakes, and serve straight from the skillet.
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