Peel the potatoes, then cook them in a large pot of water for 25 to 30 minutes, until they are tender.
Drain the potatoes and mash them until you have a smooth purée.
Stir in the butter, cream, crushed garlic, a pinch of salt, and pepper. Mix thoroughly.
Cut the tomme into thin slices or strips.
Heat the mashed potatoes over low heat, then gradually add the cheese.
Stir the mixture with a large wooden spoon for at least 15 minutes. Use a figure-eight motion and lift the mixture out of the pan periodically until it reaches a smooth, elastic, and stretchy texture that pulls away from the sides of the pan.
Spoon the aligot onto the plates, forming long, stringy ribbons.
