Pre-heat your oven to 375 degrees. Line a baking sheet with parchment.
Arrange the prosciutto in an even layer on the prepared baking sheet. Bake for 15 minutes until browned and crispy. Remove from the oven and let cool slightly.
Place the arugula in small bowl. Add 1 teaspoon olive oil, a pinch of salt and few cranks of fresh ground pepper. Toss to coat, and briefly set aside.
In a medium mixing bowl, whisk together the eggs until lightly frothy. Stir in the sun-dried tomatoes.
Heat the remaining teaspoon of olive oil in a medium non-stick pan over medium heat. Have your goat cheese ready in a small bowl by the stove. When hot, add the eggs and immediately turn the heat down to low. (We want to cook these eggs very gently, people.) Using a spatula, repeatedly pull the eggs toward the center of the pan to form small curds. When the eggs are beginning to set (after 3-4 minutes), add the goat cheese and a good pinch of salt, and continue scrambling your eggs. Cook for another 2-3 minutes until the eggs are just set but still very soft and immediately transfer them to a bowl or plate. (The eggs will continue cooking after you remove them from the pan, so be super careful not to overcook them.)
Toast your English muffins! (Don’t have a toaster? Neither do I. Just put the muffins on a baking sheet and pop them under the broiler for a couple minutes.) Feel free to butter these beauties if you’re so inclined.
Time to assemble your fancy sandwiches! I like to set up a little assembly line. Muffins, prosciutto, eggs, arugula. Break the prosciutto pieces in half—each sandwich gets 3 halves. Place the prosciutto on the bottom half of each English muffin. Add a quarter of the eggs (this will seem like a lot, but it’s a sandwich…they’ll squish down), and a quarter of the arugula. Close the sandwiches with the top half of the English muffins. Serve warm.