Preheat the grill to high. Place the sausage and shallot in the food processor. Pulse until finely ground. Add the egg and pulse again. Pour the sausage mixture into a large bowl, followed by the ground beef, 1/2 teaspoon salt and 1/2 teaspoon pepper. Mix well then gently mix in the crumbled blue cheese.
Scoop sixteen 1/4-cup portions of meat mixture onto wax paper. Press them flat with the bottom on a glass, then reform the edges so the are tight.
Grill the patties for 2 minutes per side. Meanwhile, mix the mayo and mustard together. Slice the roll in half and spread the mustard sauce on the tops and bottoms.
Layer the burgers with arugula leaves (or sprouts), the patties, and thinly sliced pickle okra.