The provincial French version of this dish is the Auvergnois aligot, for which you add cantal cheese to mash, stirring over heat until the mixture is glistening, with the texture of soft, degradable chewing gum (if you see what I mean). There are all sorts of variations. I sometimes add lardons. Nigel Slater, in the Kitchen Diaries, has a delicious, baked version with blue cheese and onions. The version below (for two) is comfort food for a cold evening.
4 medium potatoes
1 garlic clove
25 g butter
Plateful (150 g to 200 g, according to taste) cheddar
2 tbsp breadcrumbs, mixed with 1 tbsp parmesan
Peel the potatoes, and cut them into chunks about 2 cm square. (I cut the potatoes crosswise into three, then divide each section into three or four chunks.) Put them, with the garlic clove, into cold, unsalted water, and simmer gently until soft.
Note: I think that I gave bad advice when I suggested, on the grounds that salt speeds softening, that you salt the water when you make mashed potatoes. Parts of the potato are more likely to become mushy, producing a gluey result. For an entertaining account of the search for perfect mash, read Jeffrey Steingarten's essay on the subject in The Man Who Ate Everything.
Back to the pie. Drain the potatoes, return them to the dry, hot pan to steam for five minutes, and mash them. I sometimes use a masher; more often, a vegetable mill (mine's a Mouli-legumes). Stir in the cheese and butter, and season with ground black pepper and a grating or two of nutmeg. Owing to the quantity of salty cheese, you probably do not need more salt.
Pile the cheesy mash into an oven dish, sprinkle with the breadcrumbs and parmesan, and bake at gas mark 6/200 C for 20 minutes, or until the topping is brown.