Preheat oven to 400 degrees. On the stove top, heat olive oil in a saute pan over medium high heat. Add garlic and saute for 2-3 minutes. Remove shrimp from their shells and add to saute pan. Reduce heat to medium and cook shrimp for 3-4 minutes on each side until shrimp is no longer opaque. Remove from heat.
In a food processor, add shrimp and process for a few seconds until shrimp is chopped into small pieces. If you don't have a food processor, chop cooked shrimp on a cutting board into small pieces. Repeat for the chorizo!
In a medium sized bowl mix together bread crumbs, mayo, egg white, onions, and lemon juice. Next lightly fold in chopped shrimp and chorizo.
Cover bowl and place in the refrigerator for no less than 30 minutes. It is important to refrigerate the mixture so the flavors marinate and also so you can easily form patties.
In a glass baking dish, form 4 burger patties and bake uncovered for 20 minutes. While the burgers are baking, lightly toast the rolls. Assemble burgers and garnish with tomato, arugula and lemon!