Step 1

In a small bowl, combine the milk, water, yeast and sugar. Lightly whisk and let sit until bubbly and the yeast is bloomed, about 5 minutes. Add the oil.

Step 2

Mix the all-purpose flour and salt in a stand mixer fitted with a dough hook. Set the mixer to medium-low speed and slowly add the yeast mixture until entirely incorporated, scraping down the sides of the bowl to get everything homogenous. Knead on medium low until the dough is glossy and forms a rough ball, about 5 minutes. Place the dough in a lightly oiled bowl and cover with plastic wrap. Set it in a warm part of the kitchen until doubled in size, about 2 hours.

Step 3

Place a pizza stone on the bottom rack of the oven and preheat to 450 degrees F.

Step 4

Split the dough into 2 balls. On a lightly floured surface, roll one of the balls of dough as THIN as possible with a rolling pin. To get an even “trimmed” circle, use a large round lid to trim a rim around the dough. Sprinkle some semolina flour on a pizza peel. Carefully transfer the round of dough to the peel. Dock the crust with a fork or docker, poking holes all over the surface to keep it thin and crispy.

Step 5

Working quickly, add half of the pizza sauce almost all of the way to the edge of the crust, leaving about a 1-inch border. For the pepperoni side, place an even layer of pepperoni directly on top of the sauce on half of the pizza. Combine the skim- and whole-milk mozzarella in a large bowl and top the entire pizza with half of the cheese. Top the pepperoni side with some more scattered rounds of pepperoni. For the sausage side, spread half of the giardiniera on top of the cheese, then dollop with hunks of the Italian sausage on top. Transfer to the pizza stone in the oven and bake until golden and bubbly, 12 to 15 minutes. Transfer the pizza to a cutting board with the pizza peel. Make another pizza with the remaining ingredients.

Step 6

Let the pizza rest for 4 or 5 minutes, then cut into small squares--never triangles. This is called the party cut. Why? Because no matter what’s going on, when you’re eating Chicago thin crust, it’s always a big ol’ party.