Slowly pour the polenta in while whisking at the same time. Turn the heat to a low simmer, cook until the liquid mostly evaporates and the polenta is very thick. Refer to the directions on the package. Stir occasionally so it doesn’t stick to the bottom of the pan. Remove from the heat.
Stir in the parmesan, parsley, and season with salt and pepper to taste. Place the polenta into a small baking dish or ramekin depending upon the amount of portions you are making so it is about 3/4 inch. Place in the refrigerator to cool completely, about 2 hours or more if needed. (Can be made 1 day in advance. Polenta should be firm to the touch once cooled, not watery or mushy)
Once cooled cut the polenta into rectangles or your preferred shape.
Heat the oil in a nonstick pan over medium high heat. Sear both sides of the polenta cakes to golden brown and crisp. Serve immediately.