Crust: 6 Tbsp. solid vegetable shortening 1/4-lb. (1 stick) unsalted butter 2 1/4 c. all-purpose flour 1/2 tsp. ground cayenne pepper 1/2 tsp. salt 1 tsp. sugar 1 c. (4-oz.) grated smoked Wisconsin Baby Swiss cheese 7 Tbsp. ice-cold water
Filling: 3-qts. salted water 6 c. chopped fresh greens, such as turnip, Swiss chard, or spinach 8-oz. sliced mushrooms, such as chanterelles, oyster, shiitake, or crimini 1 Tbsp. olive oil 1 1/2 c. chopped onions 1/2 c. all-purpose flour 1/4 c. butter 1 c. warm milk 1 c. warm half-and-half 1 1/2 tsp. salt 1/2 tsp. freshly ground pepper 1/2 tsp. cayenne 1/4 tsp. freshly grated nutmeg 1/2 c. grated Swiss cheese 2 Tbsp. lemon juice 1 egg yolk 1 Tbsp. cream
For the crust, flatten the shortening into a disk on a piece of plastic wrap; wrap and freeze. Cut the unsalted butter into small cubes; wrap and freeze for 1/2 hour. Place the flour, cayenne, salt, and sugar in a food processor and pulse 2 times for 1 to 2 seconds each time. Scatter the frozen butter cubes over the flour and pulse about 8 times. Break up the frozen shortening over the flour mixture and pulse 6 times. Add the cheese and pulse 3 times. Pour the cold water over the pastry mixture and pulse 6 to 8 times, just until the dough comes together. Place the pastry on a floured surface, pressing to form a ball. Divide and shape the dough into 2 disks, one slightly larger than the other. Wrap in plastic wrap and refrigerate for at least 1 hour and up to 3 days.
For the filling, bring 3-quarts of salted water to a boil. Boil the greens for 3 minutes. Drain and plunge the greens into ice water. Drain well, squeezing all of the water out of the greens. Set aside. In a 5-quart Dutch oven, sauté the mushrooms in the olive oil over high heat until softened, 2 to 3 minutes. Remove from the pot; set aside.\nAdd the butter and onions to the pot. Sauté 4 to 5 minutes or until the onions are translucent. Sprinkle flour over the onions. Stir and cook 2 minutes. Slowly stir in the warm milk and half-and-half. Cook until bubbly and thick, stirring constantly. Stir in the salt, pepper, cayenne, and nutmeg. Remove from the heat. Stir in the greens and mushrooms. Add the cheese and lemon juice, and stir. Cool 30 minutes.
To complete the pie, heat the oven to 350° F. On a floured surface, roll out the larger disk to an 11-inch circle. Press into a 9-inch pie plate. Roll the other disk to a 9 1/2-inch circle. Pour the filling into the prepared pie crust. Top with the smaller crust. Trim the edges and crimp. Mix the egg yolk and cream. Brush over the top of the pie crust. Cut 5 slits in the top crust. Place the pie on a baking sheet. Bake for 30 minutes. Reduce the oven temperature to 325° F. Bake for 40 to 50 minutes longer, until the pie is golden brown. Allow the pie to rest at least 20 minutes before cutting.