Bring water to a boil in a saucepan. Add salt to taste and return to a rapid boil. Slowly whisk the polenta and stir for approximately 5 minutes. Stir in butter.
Spray an oven dish or sheet pan with nonstick cooking spray. Pour polenta into dish and spread evenly to make a 1/2-inch layer. Chill in refrigerator for about 1 hour. Punch out heart shapes with the cookie cutter and set aside.
Heat a nonstick skillet on medium heat. Add the olive oil and sear polenta hearts until golden on both sides and heated throughout.