Lamb and Broccoli Stew

Name: Lamb and Broccoli Stew
Ingredients: ¼ cup sugar; ¾ cup kosher salt plus more; 2 pounds bone-in lamb shoulder; 2 tablespoons vegetable oil; 4 medium onions, coarsely chopped; 4 garlic cloves, chopped; 1 sprig rosemary; 1 sprig thyme; 1 bay leaf; 1 cup dry white wine; 8 cups low-sodium chicken broth; 2 large eggs; 2 garlic cloves; 3 tablespoons (or more) fresh lemon juice; ½ teaspoon kosher salt plus more; ¾ cup vegetable oil; 1 bunch broccoli, stems reserved for another use, cut into small florets; Flat-leaf parsley and fresh tarragon leaves (for garnish)