For the tomato sauce: In a large bowl, add the tomatoes, parsley, olive oil, Parmigiano, dried basil, dried oregano, chili flakes, fresh basil, garlic and lots of cracked pepper, and crush with hands to mix. Cover and let sit in the fridge for 3 hours to overnight.
For the dough: In a medium bowl, mix the yeast with the warm water and let sit for 5 minutes. Add 2 tablespoons olive oil, salt and sugar and whisk. Set aside.
In a large bowl, mix the all-purpose and whole wheat flours. Make a hole in the middle and pour in the yeast mixture. Slowly hand mix the flour until all the liquid is absorbed. If too wet, add more flour, 1/4 cup at a time. Sprinkle a clean work station with flour and knead the dough until smooth and elastic. Coat a large ceramic bowl with the remaining olive oil. Place the dough in the ceramic bowl and flip over to coat in the oil. Cover the top of the dough with plastic wrap and cover the bowl with a dish towel. Let rise until the dough has doubled in size, 2 hours. Punch down the dough and let rise for another hour.
Preheat the oven to 475 degrees F.
Grease the pizza pan with the leaf lard. Mold the dough into the shape of the pan. Spoon 2 tablespoons of the sauce onto the dough. Place the pizza on the bottom oven rack for 5 minutes, to pre-crisp the crust. Take out of the oven and add another 1/4 cup of the tomato sauce. Add the mozzarella, salami, olives and pecorino.
Place the pizza on the middle oven rack and cook until the cheese is bubbly, 10 to 12 minutes. Remove from the oven. Immediately remove the pizza from the pan and sprinkle with the spinach. Cut into rectangles.