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 Cup 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; 2 Tablespoons red wine vinegar; 2 Tablespoons lemon juice; 1 Tablespoon minced shallots; 1 Tablespoon minced chives; 1 Tablespoon minced parsley; 1 Teaspoon Dijon mustard; 1 Teaspoon honey; 2/3 Cups extra-virgin olive oil