Line a 9x9 inch pan with aluminum foil and spray with nonstick spray.
In a large pot, heat butter, sugar, and sour cream over medium heat, stirring until sugar is dissolved. Bring to a boil and cook, stirring frequently, until a candy thermometer reads 234F (soft ball stage), about 5 minutes.
Remove from heat. Stir in chopped white chocolate and marshmallow cream. Stir until everything is melted and combined. It will be thick and take awhile. Fold in peppermint extract and crushed peppermints.
Pour into the prepared pan and rotate pan so the fudge reaches the corners. Chill at least 4 hours before cutting into 36 pieces.