Preheat a wood fire or outdoor charcoal grill to medium heat. 

In a Dutch oven, placed on the grill grate or directly on the embers of the fire, heat vegetable oil. 

Season roast with salt and pepper. Rub minced garlic all over surface of roast. When oil is hot, place roast fat side down in Dutch oven. Pour mushrooms over roast and cover. Cook with coals or embers on the lid and a small amount under the oven. 

Cook until meat shreds easily, about 12 hours, adding coals or wood as necessary to maintain a constant temperature. Shred meat with 2 forks and return to pot. Add barbecue sauce and mix well. Serve open-faced over Dutch Oven Sourdough Biscuits.

Dutch Oven Sourdough Biscuits:

Preheat a wood fire or outdoor charcoal grill to medium heat. 

In a mixing bowl, combine flour, baking powder, sugar and salt. Using a pastry blender or your fingertips, rub shortening into dry ingredients until the mixture resembles coarse meal. 

Combine sourdough sponge and milk. Add to the dry ingredients and mix until dough no longer sticks to the side of the bowl. 

Turn dough out onto a floured countertop. Flour fingertips and knead about 12 to 15 times. Roll out dough with a rolling pin to a 1/2 to 3/4-inch thickness. Using a 3-inch round biscuit cutter (or an empty can or glass), cut biscuits and place in a large Dutch oven with sides touching. Bake with coals on the lid and a small amount under the oven until biscuits are puffed and golden, about 15 to 20 minutes. 

Sourdough Sponge:

Mix flour and water used to cook potatoes in. Let mixture stand in a warm place covered with a dish towel for 3 days, or until bubbly and sour smelling. This is your starter. Use as directed in recipe.