Heat the oil in a medium, cast-iron skillet over medium heat. Add the onion and cook until they begin to lose their raw look, 3 to 4 minutes. Add the mushrooms and dill and cook until mushrooms are heated through, 3 to 4 minutes. Drain off any liquids. In a separate bowl, whisk eggs with salt, nutmeg and 1/2 teaspoon fresh ground pepper. Pour over the mushroom mixture and stir to mix. Cook over medium low heat, pushing dry edges to center as it cooks. When center is still damp, slip under a preheated broiler and cook until top is beginning to brown. Cut into wedges. Serve with a tomato or savory salsa.