1 Preheat oven to 350 degrees F (175 degrees C). 2  Put 1 egg in each of 12 muffin cups. 3  Bake in preheated oven for 30 minutes. 4  Plunge baked eggs in a large bowl filled with ice water until cooled completely, about 10 minutes.eady In. 1  Preheat oven to 350 degrees F (175 degrees C). 2  Put 1 egg in each of 12 muffin cups. 3  Bake in preheated oven for 30 minutes. 4  Plunge baked eggs in a large bowl filled with ice water until cooled completely, about 10 minutes.