In a small bowl, stir together the pesto and mayonnaise until smooth. Set aside.

In a skillet over medium heat, cook sausage patties for 8 - 10 minutes, or until patties reach 165˚F, turning once. Remove from heat.

While sausage patties are cooking, prepare eggs. In a soufflé dish or small bowl, whisk one egg with 1 tablespoon milk and salt & pepper. Microwave 1 minute. Let cool before removing from dish. Repeat for remaining eggs.

To assemble sandwiches, layer each bun with pesto sauce, tomato slice, egg patty, sausage patty, and arugula.