In your stand mixer or large bowl, combine water, sugar, yeast, and one cup of flour. Gently combine and let stand for 5 minutes.
Following the rest period begin to mix (use the hook attachment on your stand mixer) on low. Gently pour in remaining flour, melted butter, salt, and oil. Let mix for 8 minutes on medium low speed (scraping the bowl as needed to keep the dough in the bowl). The dough will be very tacky, that's good!
Transfer dough to a large bowl (sprayed with non-stick will help) and let rise in the fridge overnight.
As dough rises, combine olive oil, tomato paste, garlic, and a pinch of salt into small saucepot. Cook on low, stirring constantly, for 5 minutes. Add in crushed tomatoes and Italian seasoning and bring to just a simmer, whisking to melt in tomato paste. Simmer covered on low for 30! minutes, then chill for future use.
Remove dough from fridge 2-3 hours before cooking.
Preheat oven to 475 deg F and move a rack to the lower 1/3 of the oven. Grease the cast iron pan liberally with the shortening; you will use just shy of ¼ cup. Move the dough onto a floured surface and form into a 12” circle. Move the dough into the pan, press it into the sides to form the slightest of crusts, and let rise for another 30 minutes.
Following the bench proof, top pizza with 1 ½ cups of sauce and the cheese, pushing the cheese right out to the pan. Finish with any toppings and the parmesan. Bake the pizza for 14-16 minutes or until deeply golden and charred around the edges.
Once cooked, use a butter knife to free the pizza from the sides of the pan. Transfer to a cutting board, cut into slices, and devour.