Whisk the egg whites with an electric whisk or in a stand mixer for 2-3 mins, or until very foamy and doubled in size. With the motor running, add the sugar 1 tbsp at a time, beating in fully before adding the next spoonful.
When all the sugar has been incorporated, add the peppermint extract and whisk for 2-3 mins more until very thick, glossy, and holding stiff peaks.
Fit two piping bags with 1cm round nozzles, and paint a few stripes of the food colouring gels onto the inside of the bags using a cocktail stick. (Use one colour for each bag, or alternate the colours in the bags). Heat the oven to 120C/100C fan/gas ½, and line two or three baking sheets with baking parchment.
Divide the meringue mixture between the two piping bags and pipe roughly 10cm-long, 2cm-thick cane shapes onto the prepared sheets, leaving a gap between each. Bake for 50 mins until dry and crisp. Leave to cool on the sheets for a few minutes, then carefully loosen them from the parchment with a palette knife, and transfer to a wire rack to cool completely. Use the meringue canes to decorate your tree, or keep in an airtight container for up to two weeks.