Mix dry ingredients: Blend flour, sugar, salt, and yeast in a processor or bowl
Add liquids: Slowly pour in ice water and oil while mixing. Form a shaggy dough
Knead: If using a machine, knead for 3-4 minutes. By hand? Knead on oiled counter for 8-10 minutes until smooth and springy
Initial rest: Cover in oiled bowl. Let sit 30 minutes
Portion and chill: Divide into two balls. Refrigerate for 24-72 hours
Blend sauce: Pulse tomatoes, garlic, salt, herbs, and sugar. Keep chunky
Chill sauce: Refrigerate
Preheat: Oven to 500-550°F (260-290°C) with stone for 1 hour
Temper dough: Warm up for 2 hours
Stretch: To 14 inches, thin center
Prep: Add sauce, cheese on dusted peel
Bake: 6-8 minutes
Finish: Drizzle oil, slice, serve