Cube cold butter and cold lard into small pieces. Keep them in the fridge until the moment you need them — cold fat is everything for a flaky crust.
Weigh out all-purpose flour, whole wheat flour, and salt into a very large bowl. Whisk together until evenly combined.
Add roughly half the dry mixture and half the chilled fat to the food processor. Pulse in short bursts — 5 to 8 quick pulses — until the mixture resembles small pebbles or peas. You want visible chunks of fat, not a fine meal. Stop before it looks uniform. Transfer back to the large bowl.
Repeat with the remaining dry mixture and fat. Same approach — short bursts, stop at pebbles. Add to the bowl with the first batch.
In a small bowl whisk together egg, white vinegar and ice cold water. Add to the flour and fat mixture and fold to combine.
Gradually drizzle in more cold water if you need, up to a 1/2 cup more, folding gently with a spatula or your hands after each addition. Add just enough that the dough starts to come together and holds when pressed — slightly sticky but not wet. Do not overwork it. Visible streaks of fat are exactly what you want.
Turn the dough out onto a lightly floured surface. Pat into a large rectangle and divide into 6 equal portions (weighing around 300g each). Shape each into a round disk, dusting with flour as needed.
Place each disk into a small ziplock bag or wrap with cling wrap. Label with the date and freeze for up to 3 months. Thaw in the fridge overnight or on the counter before using.