Brined Grilled Asparagus with Preserved Lemon Aïoli

Name: Brined Grilled Asparagus with Preserved Lemon Aïoli
Yield: Serves 4 to 6
Ingredients: 2 pounds, thick asparagus spears, trimmed; 4 cups plus 1 tablespoon plus 2 tablespoons, water, divided; ½ cup, kosher salt; ¼ cup preserved, lemon, chopped coarse; 3 , large egg yolks; 1 , garlic clove, minced; ½ cup, vegetable oil; 1 tablespoon, lemon juice; ¼ cup, sliced almonds, toasted