How to Make It
To make the crust, combine both flours in a large bowl; add butter to flour and incorporate the butter into the flour mixture with your fingertips until small pea-size pieces form.
Combine the water, lard, and salt in a small saucepan over medium heat; cook, stirring often, until melted and combined. Carefully pour the lard mixture over flour mixture and stir with a fork until liquid is evenly distributed.
Transfer dough to a floured surface and divide into 2 equal pieces. Form each piece into (1-inch-thick) discs. Wrap each disk in plastic wrap and refrigerate for 20 minutes.
While dough is chilling, make the filling. Heat a medium skillet over high heat; add the mushrooms and cook for 3 minutes, stirring frequently. Add the oil, garlic, and green onion to pan; cook for 3 minutes, stirring frequently. Remove from the heat; combine mushroom mixture well with the rice, ground chuck, salt, and pepper in a large bowl. Divide meat mixture into 6 even portions (about 3 ounces each); gently roll each portion into a ball.
On a well-floured surface, roll each dough disc out to 1/8-inch thickness; cut dough into 6 (5-inch) circles and 6 (5-inch) circles.
Preheat oven to 400°. Make a cut in a 5-inch dough circle from an edge to center of circle. Carefully place circle in the cup of a popover pan, push and fold until sides of cup are covered; repeat with remaining 5 (5-inch) dough circles. Trim any excess dough so tops are even circles. Place 1 portion of meat mixture in each pop over crust; brush edges of dough with egg wash. Place a 5-inch dough circle on top of each pie and press edges down with fork. Brush top crusts with remaining egg wash; poke a small hole in the center of top crust. Bake at 400° until tops are golden and a meat thermometer inserted into the pie reads 145°, about 30-35 minutes.