Line a sheet tray with foil and coat with cooking spray.
Bring 7 cups of water and salt to a boil.
Add polenta in a slow stream while whisking continuously to avoid lumps.
Turn heat to low and continue to stir with a wooden spoon until polenta thickens, 5-8 minutes (you may add more boiling water as needed to keep the polenta a smooth consistency).
Turn the heat off and add parmesan and butter. Stir to combine.
Pour onto a sheet tray and spread with the back of a spoon to cover the tray evenly. Cool.
Refrigerate the polenta for 30 minutes or covered up to 2 days.
Remove the sheet tray from the refrigerator and use cookie cutters to stamp out shapes.
Heat 1 tbsp of butter in a saute pan over medium heat and cook the polenta shapes for 3-5 minutes on each side or until golden (you can also serve these cold).
Eat polenta shapes on their own or serve with a red sauce.