For Cheese spread: In medium bowl, combine all Cheddar Cheese Avocado ingredients, blending gently just until combined. Set aside.
For Salsa: Preheat oven to 350°F. Toss shrimp, olive oil, oregano, garlic, salt and pepper on a rimmed sheet pan. With a spoon or your hands, toss gently just to combine. Bake until shrimp is pink and firm, about 8 to 10 minutes. Remove from oven, coarsely chop and set aside until cool to the touch. Add remaining salsa ingredients to shrimp (kiwis through lime juice). Gently stir just to blend. Cover and set aside.
For Burgers: in medium bowl, gently combine beef, grated onion and garlic, salt and pepper. Shape into 4 equal patties, about 6 ounces each. Preheat a grill or cast-iron grill pan to high. Grill until golden brown and slightly charred, turning once (7 minutes for medium-rare). During the last few minutes of cooking top each burger with two Chipotle and Onion Cheese slices.
To assemble: spread inside tops and bottoms of brioche buns with Cheddar Cheese Avocado Sauce. Top bottom buns with grilled burger and Kiwi Shrimp Salsa; topping with bun tops. Serve immediately. Serves 4