How to Make It
Heat grill to medium-high. Once it is hot, clean the grill grate with a wire brush. Just before grilling, oil the grill grate with canola oil.
Combine the cucumber, beet, olive oil, vinegar, dill, and ¼ teaspoon each salt and pepper in a medium bowl.
Combine the mayonnaise and harissa in a small bowl.
In a separate bowl, gently mix together the beef, cumin, garlic, ¾ teaspoon salt, and ½ teaspoon pepper with your hands until just combined. Form the beef mixture into four ¾-inch-thick patties. Use your fingers to make a shallow well in the top of each patty. (This will prevent overplumping during cooking.)
Grill the burgers until an instant-read thermometer inserted in the center registers 140° F, 4 to 5 minutes per side for medium-rare. Grill the rolls, split-side down, until toasted, 10 to 20 seconds.
Stack the harissa mayo, burgers, and lettuce between the rolls and serve with the salad.