Light Fluffy Egg Soufflé Sandwich

Name: Light & Fluffy Egg Soufflé Sandwich
Ingredients: Cooking spray or unsalted butter; 8 large eggs; 1/2 cup whole or 2% milk; 1/2 teaspoon kosher salt; 3 cups hot tap water; 4 ounces Gruyère or sharp cheddar cheese, shredded (about 1 cup); 3 ounces jarred peppadew peppers; 2 tablespoons Dijon mustard; 2 tablespoons mayonnaise; 4 brioche sandwich rolls; 1 packed cup baby arugula (about 1 ounce)