Prepare creamy polenta according to the instructions stated in the package. Lightly oil a 12 x 9-inch baking dish. Transfer the hot polenta to the prepared baking dish, spreading evenly to about 3/4 to 1-inch thick. Refrigerate until cold and firm, (about 4-6 hours). Note: If using a store-bought polenta, slice the polenta in 3/4 to 1-inch thick circles then follow the instructions below.
Preheat the oven to 250 degrees.
Cut the polenta into star shapes using a small cookie cutter. Heat enough oil to lightly cover the bottom of a large skillet over medium-high heat. Working in batches (do not overcrowd the pan or else the polenta will steam instead of browning), pan fry the polenta pieces until golden brown on both sides, about 3-5 minutes per side.
Using a metal spatula, transfer carefully the polenta pieces to paper towels and drain.
Place the polenta pieces on a baking sheet and keep warm in the oven while cooking the remaining batches.
Transfer the fried polenta pieces to a serving platter. Top the fried polenta with tomato halves, a few leaves of basil, crumbled goat cheese, and a dash of salt. Serve immediately.