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For the dough: Mix the wheat berry flour, barley and 30 3/4 ounces (870 grams) filtered water to make the soaker. Rest at room temperature for about 18 hours.
Add the starter to the soaker, and mix in thoroughly, then rest the dough for 40 minutes.
Add the salt and 1 1/3 ounce (40 grams) filtered water, and do a round of stretch and fold turns. Rest the dough at room temperature for 2 hours, doing stretch and fold turns every 30 minutes.
Ball up the dough and refrigerate overnight.
For the chile oil: Gently simmer the olive oil over medium-low to medium heat with both fresh and dried chiles (chef's choice!) until the flavor is developed fully, about 2 hours.
Strain the oil before use.
For the nuts: Heat a large pan over medium heat. Place the almonds and pecans in the pan and toast. Make sure to check on the nuts every few minutes by shaking them around to get all sides toasted evenly. Remove from the heat when the oils are released and before the nuts burn!
For the hummus: Place the lemon juice, oil, tahini, 1/2 cup water, the salt, pepper and garlic in a food processor and buzz for about 2 minutes. Add the garbanzo beans and process for about 10 minutes for maximum creaminess!
For the pizza: Bring the dough back to room temperature, 30 minutes to 1 hour.
Roll the dough out to about 14 inches in diameter. Brush the dough with an even layer of the za'atar oil, not too much. Place a pizza screen on top of the dough so it does not puff up in the middle while cooking. Cook the pizza for 5 to 8 minutes. When done, remove the screen and spread a thin, even layer of hummus, about 8 ounces, over the pizza. Drizzle some olive oil in a zigzag, then turn the pizza and drizzle a zigzag of chile oil as well. Sprinkle with sumac, the toasted nuts and finish with the chopped mint. Cut and serve!