In a large bowl, whisk together the all-purpose flour, salt, and pepper. Add in the chunks of butter and the lard/shortening. Using your fingertips, cut the fat into the flour until you’re left with pea-sized pieces of butter and lard/shortening coated in flour. Using the tip of a knife, stir in the ice water 2 Tbsp at a time until you can squeeze the dough together in your hands. Give the dough a couple of gentle kneads to bring it together. Divide in half and shape into two discs. Wrap in plastic wrap and chill for 3 hours to overnight.