Combine the turkey, garlic, paprika, 3/4 teaspoon salt and a few grinds of pepper in a medium bowl; mix with your hands until just combined. Form into four 1/2-inch-thick patties; set aside.
Combine 1/2 avocado, the mayonnaise, lime juice and 1/4 teaspoon salt in a medium bowl; mash until smooth. Thinly slice the remaining 1/2 avocado and season with salt and pepper. Set aside for topping.
Heat the vegetable oil in a large nonstick skillet over medium-high heat (or preheat a grill to medium high and oil the grates). Add the burgers and cook until browned, 3 to 4 minutes per side. Top each burger with a slice of cheese; cover and cook until the cheese melts, about 30 seconds.
Meanwhile, split and toast the buns; spread the avocado mayonnaise on the cut sides. Serve the burgers on the buns with lettuce, the sliced avocado and tortilla chips.
Photograph by Ryan Dausch
Courtesy of Food Network Magazine