Line two large baking sheets with parchment paper.
Break each graham cracker sheet along the center perforation to make 2 squares, 48 squares total.
Beat the peanut butter and softened butter in a large mixing bowl with an electric mixer until completely smooth. Add the vanilla and salt and mix until combined.
Gradually add the powdered sugar, mixing until a thick buckeye-style filling forms. It should be soft enough to shape but firm enough to hold its shape.
Divide the filling into 24 equal portions. Roll each into a ball, then flatten it into a square slightly smaller than a graham cracker square.
Place one peanut butter square on each of 24 graham cracker squares. Top with the remaining squares and press gently until the filling spreads almost to the edges.
Arrange the sandwiches on one prepared baking sheet and refrigerate for 30 minutes, until firm and well chilled.
Microwave the white chocolate wafers or almond bark in a deep bowl in 20 to 30 second intervals, stirring after each, until smooth.
Dip one chilled sandwich at a time, turning it with a fork until the top, bottom and sides are covered. Let the excess drip off, tap the fork on the bowl, and set it on the second baking sheet. Rewarm the coating for 10 to 15 seconds if it thickens. Let the coating set completely.
Melt the red candy melts in 20 second intervals, stirring in 1 teaspoon shortening if needed to thin. Drizzle diagonally over the squares.
Melt the green candy melts the same way with the remaining 1 teaspoon shortening if needed, and drizzle in the opposite direction.
Decorate with Christmas sprinkles while the drizzle is still wet. Let stand at room temperature 20 to 30 minutes, until fully set.