Preheat oven to 175°C/350°F. Add a decorating tip to a piping bag. With the red food coloring, draw 4 stripes up the sides of the bag.
Add egg whites and salt to a bowl. Beat the egg white mixture until foamy, then gradually add the sugar a little at a time until thick and glossy. Stir in the peppermint syrup. Transfer to piping bag.
Pipe the meringue onto a parchment-lined baking sheet in circles approx. 4 cm/1.5 in. in diameter and 2.5 cm/1 in. high. Reduce heat to 120°C/250°F and bake for approx. 2 hrs., or until the meringues are firm. Crack the oven door open with a wooden spoon and let cool and dry slowly.
Meanwhile, melt the chocolate in a heatproof bowl set over a pot filled with simmering water. Dip the bottoms of the cooled meringues in chocolate, and leave to set on a piece of parchment paper. Enjoy!