For the dough, combine flour, sugar, salt and yeast in food processor and pulse 5 to 6 times, then add EVOO and water and press on to process dough ball 15 to 20 seconds or so until just combined. Knead on lightly floured surface until dough forms a ball, about 8 to 10 minutes. Cut into 3 pieces, place in greased deli tubs or plastic containers with a little oil on top of the dough as well. Rest dough overnight in the fridge and then let rest on the counter 2 hours before making the pizzas.
For the sauce, combine all ingredients in a bowl.
For an oven preparation, preheat the oven to 550°F (or as high as your oven can go) with a pizza stone or steel or 15-inch cast-iron skillet on middle rack for 45 minutes to an hour. For tabletop pizza ovens, add fuel and follow directions per manufacturer; we used a ROCCBOX for 2 years when we lost our home and it rocked, as promised!
For the hot honey topping, place honey in a bottle and add the chili paste. Place top on bottle and run under hot tap water to thin the honey, then shake the bottle to combine the hot chili paste with the honey.
Roll out rested doughs on lightly floured surface and transfer to a peel. Top with an even and thin layer of sauce and dot pizzas with mozzarella. Sprinkle with pecorino cheese and arrange hot soppressata on top. Scatter a little red onion on each pizza and slide into oven onto hot surface and bake 3 to 4 minutes, then turn broiler on high and go 3 to 4 minutes more until brown and bubbly. Top each pizza with hot honey and basil. Cut and serve.