Egg Baked Inside a Muffin

Ingredients

• 8 eggs, room temperature
• Water and Ice
• 1 red onion, small dice
• 2 ½ cups flour
• 2 teaspoons salt, divided
• ¼ teaspoon ground black pepper
• 1 tablespoon baking powder
• ½ teaspoon baking soda
• 1 ¼ cups buttermilk
• ½ cup butter
• 1 sprig thyme, leaves minced
• 3 ounces Cheddar
• 3 ounces Gruyère
• 3 ounces Parmesan
• 1 teaspoon olive oil