Bring a large pot of salted water to a boil. Fill a large bowl with ice water. Cook the collards in the boiling water until pliable but not falling apart, 30 to 45 seconds. Transfer with tongs to the ice water and let cool, about 1 minute. Drain and pat dry.
Toss the cucumber with the vinegar, 3/4 teaspoon salt and a few grinds of pepper in a medium bowl. Mash the avocado with the hot sauce and 1/4 teaspoon salt in a small bowl.
Form the beef into four 4-inch-wide patties (about 3/4 inch thick); season generously with salt and pepper. Heat the vegetable oil in a large skillet over medium-high heat. Add the burgers and cook until browned, 3 to 4 minutes per side; top each with 2 slices cheese during the last 2 minutes of cooking and cover to melt. Transfer to a plate.
Top the burgers with the avocado mixture, red onion and alfalfa sprouts. Place 2 collard greens on a board with the stem ends overlapping, then place a burger on one short end and roll up the burger, tucking the collards around it to fully enclose. Repeat with remaining collards and burgers. Cut the burgers in half.
Toss the Peppadews with the cucumber salad and season with salt and pepper. Serve with the burgers.