In a heavy saucepan bring liquid and salt to boil over high heat. Reduce heat to medium and add the polenta gradually, whisking constantly. Continue to cook and whisk for 5 minutes, the mixture should be thick and creamy. Reduce heat to low and add cheese if using. Stir with a wooden spoon until the cheese is melted and continue to cook for 10 minutes stirring frequently. If not adding cheese then just continue to cook and stir on low for 10 minutes once you have reduced the heat.
Invert a rimmed quarter sheet baking sheet on the counter and top with parchment or waxed paper. Spread the polenta out with a spatula (a large metal off set spatula works best) into a smooth, even layer. Top with another sheet or parchment or waxed paper. Take another baking sheet the same size and place the bottom on top of the parchment or waxed paper. You will now have the polenta sandwiched between both the baking sheets. Gently press down on the top baking sheet with both hands until the polenta is even and the thickness you want, I usually do ¼ inch thick. Refrigerate for at least two hours or overnight.
Remove the top baking sheet and top layer of paper. Slide the bottom paper with the polenta on it onto a cutting broad. Cut with knife or cookie cutters into desired shape and size. I usually make triangles by cutting 3½ inch squares and then cutting the squares in half on the diagonal. If you do this you will get 24 good sized triangles.
Heat a large skillet or griddle over medium-high heat and add enough olive oil to lightly coat. Once the olive oil is heated place the polenta pieces (smoothest side down first) and fry for about 3 – 4 minutes or until golden brown. Flip and fry the other side until it is golden brown.