Finely chop half the peanuts and mix them with the sugar. Spread the mixture out onto a flat plate. On another plate, pour in a little of the vodka. Dip the rim of a martini glass into the vodka, then into the peanut and sugar mixture. Set aside while you make the cocktail.
Into a blender, add the banana, vanilla vodka and white chocolate liqueur. Blend until smooth. Pour into the prepared glass and serve.