Spring Vegetable Barigoule

Name: Spring Vegetable Barigoule
Ingredients: 1 lemon, halved; 16 baby artichokes (2 1/2 pounds); 2 parsley sprigs; 2 tarragon sprigs; 1 fresh bay leaf; 1/2 teaspoon black peppercorns; 1/2 cup white wine; 2 garlic cloves, thinly sliced; 2 cups chicken stock or low-sodium broth; 1 1/2 cups water; Kosher salt; 1/2 cup diced tomato; 1/4 cup minced carrot; 1/4 cup minced celery; 1/4 cup minced leek (white and light green parts only); 1/4 cup minced onion; Ice; 2 pounds thin asparagus, ends trimmed