Ingredients

• 1 1/2 cups cold water
• 1/3 cup yellow cornmeal (preferably stone-ground)
• 1/4 teaspoon salt
• 2 small (2 1/2-inch-wide) tomatoes
• 1 1/2 oz smoked mozzarella, coarsely grated (1/3 cup)
• 1 cup fresh basil
• 2 tablespoons water
• 1 small garlic clove
• 1 teaspoon fresh lemon juice
• 1 teaspoon extra-virgin olive oil
• Pinch of sugar
• Special equipment: a 2 1/2-inch round cookie cutter

Instructions

1. Whisk together water, cornmeal, and salt in a 1-quart heavy saucepan and bring to a boil over moderate heat, whisking constantly. Reduce heat to low and cook, stirring frequently, until very thick, 15 to 20 minutes.
2. Spread polenta into a 10- by 5-inch rectangle on a lightly oiled baking sheet. Chill, uncovered, until firm, about 1 hour.
3. Prepare grill for cooking.
4. Drain tomatoes while polenta is chilling: Cut 4 (1/4-inch-thick) crosswise slices from middle of each tomato. Sandwich slices between triple thicknesses of paper towel and press gently to absorb excess moisture. Preheat oven to 400°F.
5. Cut 4 (1/4-inch-thick) crosswise slices from middle of each tomato. Sandwich slices between triple thicknesses of paper towel and press gently to absorb excess moisture.
6. Preheat oven to 400°F.
7. Grill polenta: Cut out 8 (2 1/2-inch) rounds from polenta with cookie cutter. When fire is medium-hot (you can hold your hand 5 inches above rack for 3 to 4 seconds), grill polenta rounds in a grill basket until crusty, about 5 minutes on each side. Transfer to an ungreased baking sheet.
8. Cut out 8 (2 1/2-inch) rounds from polenta with cookie cutter. When fire is medium-hot (you can hold your hand 5 inches above rack for 3 to 4 seconds), grill polenta rounds in a grill basket until crusty, about 5 minutes on each side. Transfer to an ungreased baking sheet.
9. Assemble and bake stacks: Season tomato slices with salt and pepper and sprinkle with cheese. Assemble 4 stacks by placing a tomato slice on top of each of 4 polenta rounds (use a spatula to transfer tomato slices), then top each with another polenta round and tomato slice. Bake in middle of oven until hot and cheese is melted, about 15 minutes.
10. Season tomato slices with salt and pepper and sprinkle with cheese. Assemble 4 stacks by placing a tomato slice on top of each of 4 polenta rounds (use a spatula to transfer tomato slices), then top each with another polenta round and tomato slice.
11. Bake in middle of oven until hot and cheese is melted, about 15 minutes.
12. Make sauce while stacks bake: Purée basil, water, garlic, lemon juice, oil, and sugar in a blender, scraping down sides frequently, until smooth. Season with salt and pepper.
13. Purée basil, water, garlic, lemon juice, oil, and sugar in a blender, scraping down sides frequently, until smooth. Season with salt and pepper.
14. Serve stacks with basil sauce.