Prepare the waffle batter: In a bowl, whisk the flour, baking soda, baking powder and salt together. In a separate bowl, whisk the eggs, melted butter and buttermilk. Slowly whisk the wet ingredients into the flour mixture. Set aside.
Prepare the crispy prosciutto: Preheat oven to 400°F. Lay the prosciutto flat on a baking sheet, with a little space between them. Place in the oven and bake for 12—15 minutes, until the prosciutto gets crispy. Remove from oven and set aside.
Make the sandwiches: Set oven to 425°F. Pour your waffle batter into the sandwich molds of an egg sandwich pan.
Crack the eggs into the egg molds of the pan. Sprinkle the basil over the top of the eggs, season with salt and pepper and top with cheddar. Bake for 8—10 minutes, until the buns are crispy and eggs are cooked. Sandwich an egg and prosciutto slice between two buns and serve immediately.