This is my take on Shepherd's Pie, but as my father will quickly point out, Shepherd's Pie is made with Mutton, not Chevon.
Peel and cube the potatoes, then steam until tender. Mash the potatoes with the 1/4 C butter and 1/2 t salt.
As soon as the potatoes are done steaming, place the broccoli in steamer and steam 7-10 minutes. It should be al dente, as it will cook a bit more in the oven.
In a cast iron skillet, saute mushroom and shallot until tender. Place in a bowl and set aside. In the same skillet, cook the chevon (lightly salted with 1/2 t salt) until the chevon is no longer pink. Drain the grease if there is any, and mix the meat with the mushrooms and onions.
Meanwhile, in a saucepan whisk the arrowroot powder with water. Gently heat until it begins to thicken. Add the milk and heat until thickened, whisking frequently. Stir in the salt and nutmeg.
Combine the milk with the chevon mixture, and place in the bottom of a casserole dish or large pie plate. Place the steamed broccoli on top of the chevon mixture. Cover all with the mashed potatoes, spreading them out to the edges of the dish. Top with the grated cheese.
Bake in a 350° oven for 15-20 minutes or until cheese is melted and starting to brown.