Lamb Sliders with Tzatziki

Name: Lamb Sliders with Tzatziki
Ingredients: 1 large beet; 1 teaspoon sugar; 1 tablespoon butter; 3 cloves garlic; 2 tablespoons red wine vinegar; 1 cucumber, peeled and seeded; 1 cup Greek yogurt; 1 tablespoon chopped fresh dill; Lemon juice, as needed; Salt and ground white pepper; 1 pound ground lamb; 1 tablespoon chopped fresh mint; 1 tablespoon chopped fresh oregano; 1/4 cup feta; 1/2 teaspoon ground cumin; 1/2 Spanish onion, diced; 1/2 jalapeno, seeded and finely diced; Salt and freshly ground black pepper; 4 to 6 mini potato buns, for serving