Bring a large saucepan of salted water to a boil. Add the potatoes and pars-nips and cook for about 12 minutes, until they are al dente. Drain in a sieve and let the liquid evaporate. Slide them into a baking dish.
Melt the butter in a saucepan, stir in the flour, and cook for about 3 minutes. Stir in the milk and keep stirring—with a whisk—until you have a smooth sauce. Don’t worry if your sauce has lumps at first, keep stirring: It will smooth out.
While stirring, allow the sauce to reduce until it has the consistency of thin yogurt. Season with the mustard, vinegar, thyme, salt and pepper. Pour the sauce over the vegetable cubes in the baking dish.
Mix the breadcrumbs with the cheese and some pepper. Sprinkle the entire dish with it. You can do all of this in advance.
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