Vegetable Toad in the Hole

Name: Vegetable Toad in the Hole
Ingredients: 2 large eggs; 3/4 cup whole milk; 3/4 cup all-purpose flour; 2 tablespoons plus 1 teaspoon whole-grain mustard; 3 tablespoons vegetable oil; Sea salt; 2 small carrots, cut into 2-inch lengths; 2 tablespoons unsalted butter; 1 medium onion, cut into 1/2-inch-thick wedges; 2 garlic cloves, sliced; 2 ounces haricots verts or thin green beans; 1 cup halved cherry tomatoes; 1 tablespoon finely chopped basil; 1/2 teaspoon finely chopped thyme; 1/2 teaspoon finely chopped rosemary; Pepper