To make the dressing: Finely chop the garlic and anchovies in a food processor. Blend in the lemon juice and mustard. With the machine running, gradually blend in the oil. Season the dressing, to taste, with salt and pepper.
To make the croutons: Spread the olive oil over a small baking sheet. Transfer the hot polenta to the baking sheet, spreading evenly to form an 8 by 5 by 3/4-inch-thick rectangle. Cover and refrigerate until cold and firm, about 2 hours.
Cut the polenta into 3/4-inch cubes. Pat the polenta cubes dry with paper towels. Add enough vegetable oil to a heavy large frying pan to come 1-inch up the sides of the pan. Heat the oil over high heat. Working in batches of 10, carefully add the polenta cubes to the oil 1 at a time and fry until golden brown, stirring to keep the cubes separate, about 2 minutes. Using a slotted spoon, transfer the polenta croutons to a paper towel-lined plate to drain any excess oil.
(The dressing and polenta croutons can be prepared 1 day ahead up to this point. Cover the dressing and polenta croutons separately and refrigerate. Rewarm the polenta croutons on a baking sheet in a 350 degrees F oven before serving.)
To make the salad: Prepare the barbecue for high heat. Grill the lettuce until lightly charred, about 2 minutes per side. Cut the lettuce into bite-size pieces.
On a serving platter, mound the grilled chopped lettuce. Decoratively scatter the sun-dried tomatoes and pine nuts. Drizzle with enough dressing to evenly coat. Sprinkle Parmesan and scatter the warm polenta croutons over and serve immediately.
Bring 3 cups of water to a boil in a heavy large saucepan. Add salt. Gradually whisk in the cornmeal. Reduce the heat to low and cook until the mixture thickens and the cornmeal is tender, stirring often, about 12 to 15 minutes. Turn off the heat. Add the butter, and stir until melted.
Lightly oil a half sheet pan. Transfer the hot polenta to the prepared baking dish, spreading evenly to 3/4-inch thick. Refrigerate until cold and firm, about 2 hours.