Preheat oven to 350 degrees F.
First, make the mashed potatoes:
Start the potatoes to boil (see note below) and then continue with the rest of the recipe. In the pan the potatoes were cooked in, while potatoes are still hot, mash the potatoes. Add 2 tablespoons butter and the milk and continue to mash. Add salt and pepper. The mash should be stiff and heavy but a texture that’s spreadable. Add a little more milk if needed. Cover to keep warm while the rest of the dish is assembled.
Make the shepherd’s pie:
In a 10-inch ovenproof skillet, heat the three tablespoons butter over medium heat. Add the onions, celery, and carrots, and stir. Continue to cook, stirring often, until softened, about 8 to 10 minutes.
Sprinkle with the amount of flour needed to make the amount of gravy you need. Stir for about 2 minutes until flour begins to appear dry and incorporated. Add the amount of broth you need and stir, bring to a simmer and cook several minutes until thick enough to coat the back of a spoon. Add any additional leftover gravy and heat through. Taste and add Worcestershire sauce, a splash of wine, salt, and pepper to taste.
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