First mix: In a stand mixer fitted with the dough hook attachment, combine the water, yeast, beer, oil and 00 flour and mix for 5 minutes on low speed or until well incorporated. If you don’t have a stand mixer with a dough hook, you can mix the ingredients in a large bowl by hand:Use one hand to mix the dough until it forms a ball and all the dough has pulled away from the sides of the bowl. Transfer to a clean, dry work surface (marble or granite is fabulous) and knead, using the heels of your palm, for about 5 minutes, then stretch and flip. Repeat, until the dough can’t be stretched any more. Cover and let rest for 10 minutes.(Never let your dough get a crust from the air.)
Second mix: Return the dough to the stand mixer or bowl and add the all-purpose flour and salt. Mix for 5 minutes on medium speed. If mixing by hand, it will take about 7 minutes. The dough should form a cohesive ball and pull away cleanly from the sides of the bowl. If it is too wet and sticking to the bowl, add more flour, 1 tsp at a time. If it is too dry and not all the flour is incorporated, add more lukewarm water,1 tsp at a time, until you have a smooth, shiny dough.
Cover the bowl with plastic wrap or a plate and let rest for 20 minutes.
Divide the dough into four pieces. One at a time, cup each piece of dough in your hand and roll it around in a circle on a clean, dry work surface until you’ve formed a smooth, round ball. Place the dough balls in a large container, spaced about 4 inches apart, to allow them room to expand.
Seal the container tightly with its lid or plastic wrap and let the dough rest at room temperature for 1 hour. Then place in the fridge for at least 24 hours, and up to 72 hours. One hour before shaping and assembling the pizzas, remove the dough from the fridge and let it come to room temperature.
Form the dough: Flour your hands and transfer one ball of dough to a lightly floured work surface. Sprinkle more flour onto the dough and your hands to prevent sticking.
Starting at one side of the ball, press down with your fingertips and gently stretch it with a circular motion until it expands into a disk about6 to 8 inches in diameter. Continue massaging the dough, shaping it with your palms and fingers until the disk is about 10 inches across.Don’t worry about making a perfect circle, or making a doughy rim (aka the cornicione); this will naturally form when baking. Just go for a completely flat disk. Whatever you do, don’t overhandle the dough: be gentle with the blisters and bubbles that air will create in the crust; they will add texture and character to your final creation. Remember: no rolling pin!
Flop the dough onto a lightly floured, perforated 14-inch pizza pan (or a regular pizza pan or an inverted baking sheet, if that’s what you have) and gently pull the edges outward, leaving some space so as not to cover the pan completely. I do this so that when transferring to and from the oven, the outer crust remains undisturbed.
Assemble and bake: Follow each recipe’s method for assembly and baking instructions, topping your dough immediately with your desired toppings. Timing is critical here! Waiting too long before topping your stretched dough can result in dry dough.