In a stand mixer, mix butter and peppermint extract until fluffy. Add two cups of the powdered sugar (and salt if using) and beat until well combined. Slowly drizzle melted white chocolate into mixing bowl and beat on medium to high for one to two minutes until well combined with butter and powdered sugar mixture. Add in remaining powdered sugar and two tablespoons of half and half. Beat on high until light and fluffy. Add in additional half and half, a few drops at a time, as needed and continue mixing to reach your desired consistency.