To Allumette a vegetable means to cut it into small, thin pieces the size of matchsticks.
If the vegetable is to be cooked, an allumette cut allows for a vegetable to cook rapidly and evenly, and integrate well into a mix of other ingredients, for instance in a sauce. If the vegetable is being served raw, an allumette cut allows the cook to make a fine, delicate garnish for salads or as an ingredient in something like a salade chinoise, etc.
The technique is used on firm vegetables such as potato, celery, carrot, peppers, turnips, parsnips, etc. Onion is too difficult to apply an allumette cut to owing to its layers, and soft vegetables such as tomatoes are almost impossible. Items such as citrus peel can also cut into allumettes.
An allumette cut ends up with vegetable pieces about 3 mm x 3 mm square and 5 cm long (1/18th inch square x 2 inches.)
To do this, the first step is to peel and wash the vegetable, then regularize its shape into a rectangle or square by topping and tailing it and squaring off the sides. Then cut it into 5 cm (2 inch) long pieces, then cut each of those pieces into 3 mm (1/8th inch) thick slices. Stack those slices, then cut them lengthwise into 3 mm (1/8th inch) wide sticks.
Note: some chefs call a 3 mm x 3 mm cut a "regular julienne" cut, and define allumette as 6 mm x 6mm (1/4 inch.)
A allumette cut can also be achieved with a mandoline.