This recipe was created for Club House for Chefs by: Ryan Lachaine, Chef Owner Riel Restaurant in Houston, TX.
Preheat oven to 325°F. Combine broth, ½ chopped onion, 1 chopped garlic clove, whole peppercorns, thyme, and bay leaves in a medium pot. Add pork shoulder; season with salt and pepper. Bring to a simmer over medium heat.
Cover pot. Transfer to oven. Braise until pork shoulder is tender and shreds easily, about 2 hours. Remove from oven; let cool. Transfer pork shoulder to a work surface. Shred meat with your fingers and transfer to a medium bowl. Strain pan juices through a fine-mesh sieve; add ½ cup juices to pork; discard solids in strainer.
Melt butter in a large skillet over medium heat. Add remaining 1 chopped onion and 3 chopped garlic cloves; cook, stirring often, until soft, 5-7 minutes. Add mushrooms; cook, stirring often, until almost all liquid is evaporated, 5-7 minutes. Add wine and stir, scraping up browned bits. Bring to a boil, cook, stirring often, until liquid is almost evaporated, about 5 minutes.
Add ground pork, cinnamon, and cloves. Cook, stirring to break up into small pieces, until pork is cooked through, about 5 minutes. Add potato. Cook until potato is soft, about 10 minutes. Remove from heat. Stir in shredded pork with juices. Season to taste with salt and pepper; let cool slightly. Chill until cold, about 1 hour.
Roll out 1 dough disk on a lightly floured surface into a 12" round. Transfer to pie dish, leaving overhang. Fill with cooled meat mixture. Roll out remaining dough disk into a 10" round. Place dough over meat filling. Fold overhang over top crust and crimp edges. Brush crust with egg yolk. Cut three 2" slits in top crust. Chill for 1 hour.
Preheat oven to 400°F. Bake tourtière for 30 minutes. Reduce heat to 350°F; bake until crust is golden brown and filling is bubbling, 40-50 minutes. Let cool for 20 minutes before serving.