Veggie Burger Hash

Name: Veggie Burger Hash
Ingredients: 3 tablespoons canola oil, divided; 3 frozen veggie burger patties; 1 large sweet potato, diced (1/2-inch); 1 medium red onion, diced (1/2-inch); 4 cups chopped kale; ¼ cup water; 3 cloves garlic, finely chopped; 2 teaspoons chopped fresh thyme or 3/4 teaspoon dried, plus more for garnish; ¼ teaspoon salt; ¼ teaspoon ground pepper, plus more for garnish; ¼ cup mayonnaise; 2 tablespoons ketchup; 1 teaspoon hot sauce, or to taste; 4 large eggs