For the dough: Sprinkle the yeast over 1 1/2 cups warm (not lukewarm) water in a bowl. Let stand for a few minutes.
In a mixer with a paddle attachment, combine the flour and salt. With the mixer running on low speed, drizzle in the olive oil and mix until combined. Next, pour in the yeast/water mixture, add the pressed garlic and mix until just combined and the dough comes together in a sticky mass. Divide the dough into 2 balls and put each one in a separate ziptop bag. Set the dough aside for 1 to 2 hours, or store in the fridge until you need it.
For the chicken: Heat the olive oil in a heavy pot over medium-high heat. Season the chicken with salt and pepper and sear it on both sides until the skin is golden brown. Remove the chicken from the pot and pour off all but 1 tablespoon of the grease.
Add the onions and cook until softened, 2 to 3 minutes. Add the garlic and cook for another minute. Pour in the barbecue sauce and return the chicken to the pot. Cover and cook over medium-low heat until the chicken is falling off the bone, 45 to 50 minutes. Remove the chicken from the pot and set aside until cool enough to handle.
When cool, use 2 forks to shred the meat from the bones, discarding the skin and bones. Skim off the excess fat from the top of the sauce and reserve.
For the slaw: While the chicken is cooking, combine the shredded cabbage and sliced jalapeno in a bowl. In a separate bowl, mix the milk, mayonnaise, sugar, vinegar, cayenne and salt. Pour the dressing over the cabbage mixture and toss to combine. Cover and refrigerate.
For the pizza: When you are ready to make the pizza, preheat the oven to 475 degrees F. Oil a baking sheet or pizza pan with olive oil.
Grab one of the balls of pizza dough (the recipe makes 2 crusts, so you can refrigerate or freeze the other ball of dough for another recipe) and squeeze the dough toward the bottom to form a nice, tight, pulled ball. You can roll out the pizza with a rolling pin if you'd like, but sometimes it's just as easy to throw it around and pull and stretch until it feels right.
When the crust is nice and thin, lay it on the oiled baking sheet. Drizzle a little olive oil on the dough and spread it with your fingers. Very lightly sprinkle some salt on top. Spread the reserved barbecue sauce and onion mixture over the crust, then cover with the mozzarella slices followed by the shredded chicken. Bake on the bottom rack until the crust is golden brown and the toppings are bubbly, 12 to 15 minutes.
Stir the cilantro into the slaw. Top the pizza with the slaw, cut into pieces and serve.
It's best to make the dough at least 24 hours in advance; 3 or 4 days is even better.