Grind up the dried oregano until very fine; measure out 3 tablespoons.
Melt butter in a saucepan over medium-high heat. Lower heat to medium-low and stir in oregano. Carefully pour in water. Simmer gently, stirring every 20 minutes, until flavors combine, about 2 hours in total. Remove saucepan from heat.
Wrap a piece of cheesecloth around a glass, ceramic, or metal bowl and secure with a rubber band. Pour butter mixture through cheesecloth into bowl. Remove rubber band and carefully squeeze excess butter out of the cheesecloth, making sure oregano is strained out.
Cover bowl with aluminum foil and chill in the refrigerator until butter solidifies above water, about 4 hours. Break the butter in half with a knife and transfer to a plate. Cover. Discard water.
