THE CORNBREAD SQUARES: Prepare corn muffin mix according to package instructions, using a 9-inch square cake pan. cool and cut into 1½-inch squares, then cut in half to make tops and bottoms.
THE SLIDERS: In a large bowl, mix chorizo, beef, onion, garlic, cumin, and chili powder. Shape mixture into 2-inch patties.
Heat grill to medium-high heat. grill burgers to desired doneness—about 2 to 3 minutes per side for medium-rare, or 145°F on an instant-read thermometer. Top with cheddar and jalapeño slices, and move them away from flame. Close lid of grill and heat until cheese melts, about 1 minute. Place burgers, between cornbread halves and garnish with avocado slices and salsa.