Arrange a rack in the middle of the oven and heat to 375°F. Coat a 9x13-inch baking dish with olive oil.
Heat the oil in a large frying pan over medium heat until shimmering. Add the onion, pepper, and ½ teaspoon of the salt. Cook, stirring occasionally, until softened, about 5 minutes.
Add the spinach and garlic, and toss until wilted and almost all of the liquid is evaporated, about 3 minutes. Remove from the heat and stir in the dill. Transfer to the baking dish and spread in an even layer.
Place the eggs, milk, mustard, remaining 1 teaspoon salt, and pepper in a large bowl and whisk until the eggs are completely broken up and incorporated.
Pour over the spinach mixture in the baking dish. Sprinkle evenly with the feta.
Bake until the top is light golden-brown and a knife inserted in the middle comes out clean, 40 to 45 minutes. Let cool for 5 minutes before slicing.