Bring the water to a rolling boil in a medium saucepan. Slowly, add in the polenta, while continuously stirring. Stir for 10-15 minutes until the polenta starts to thicken. Add in the salt and milk. Stir to combine. Reduce the heat to low and stir in the butter and cheese. Once the cheese is melted, remove from the heat.

Line a 9 x 9 inch baking pan with parchment paper. Spread the polenta in one even layer over the parchment. Place in the refrigerator to chill and harden for at least an hour.

Preheat the oven to 200 degrees F.

Meanwhile, line a large baking sheet with parchment paper. Place the tomatoes on the parchment, cut side up. Drizzle the tomatoes with olive oil and a little bit of balsamic vinegar. Sprinkle with salt and pepper. Roast the tomatoes for two to three hours until dried and flat. The tomatoes will become sweeter the lower and slower they roast.

After the polenta has hardened, use a one inch round biscuit cutter ( a martini shaker top works too), to cut out little discs.

Heat the butter and olive oil in a large skillet over medium heat for two minutes. Add as many polenta discs as will fit to the pan. Cook for five to seven minutes on each side, until golden and crispy. Then flip and cook for another five to seven minutes. Once crispy and golden, add to a plate lined with a paper towel to cool.

Once all the tomatoes are roasted and the polenta discs are fried, start assembling. Add two or three tomatoes to each polenta disc. Top with fresh basil right before serving.

If feeding a crowd, you can keep the bites, minus the basil, in the warm oven until ready to serve.