Make dough: Put yeast, oil, and 2 cups plus 1 tbsp. cold tap water in bowl of a stand mixer and mix, using dough hook, on lowest speed, 5 minutes or until yeast has completely dissolved. Add flour and mix another 8 minutes.
Cover bowl loosely with a dampened towel and let dough rise 20 minutes.
Add salt and mix on low speed until incorporated and dissolved, about 7 minutes.
Turn dough onto a lightly floured work surface and cut into 6 equal portions. Roll each portion with a circular pressing motion into a tight ball. Place on a lightly floured baking sheet.
Cover tightly with plastic wrap and let rise at least 4 hours at warm room temperature. Dough balls have risen properly when they are soft, pillowy, and full of air.
Heat a pizza stone or baking sheet on lowest rack of oven at 550° (or as high as oven will go), at least 30 minutes.
Make toppings: With flat side of a chef's knife, mash a third of mozzarella until pulverized. Dice remaining mozzarella into 1/2-in. cubes. In a medium bowl, mix both mozzarellas with mozzarella liquid, caciocavallo, cream, and buttermilk. Season with 1/4 tsp. salt.
Cut broccoli rabe into 1-in. sections, discarding tough lower stems.
In a large frying pan over very low heat, cook garlic in oil, stirring often, until it starts to turn transparent, about 5 minutes. Add chile flakes and toast for a second, then add broccoli rabe. Stir in remaining 1/4 tsp. salt and several grinds of pepper.
Crank heat to medium-high and cook broccoli rabe, stirring, until liquid starts to evaporate and broccoli rabe is tender-crisp, 5 to 7 minutes (don't cook it to mush). If liquid is gone and broccoli rabe is still too crunchy, add water in 1/4-cup increments and cook until tender-crisp.
Working with 1 dough ball at a time (keep the rest tightly covered), set on a well-floured pizza peel or baking sheet. To stretch into an 11- to 12-in. circle, first tap down center of ball with your fingertips to gently deflate it. Next, push it outward from the center with your fingertips. Then pick up the dough circle and, holding it under the rim, turn it like a steering wheel, letting the gravity of the dough help it stretch. Drape the dough over the backs of your hands and gently stretch outward, rotating periodically. Flop the stretched dough down onto the pizza peel.
Spread about 2/3 cup cheese mixture evenly over dough. Top with 1/2 cup broccoli rabe, a generous pinch chile flakes, and 2 tbsp. olives. Give peel a good shake every few seconds to keep dough from sticking.
Plant tip of pizza peel (or long edge of baking sheet) on pizza stone and shove pizza quickly onto stone (or preheated sheet). Bake 5 to 6 minutes, or until puffy and browned. Drizzle with extra-virgin olive oil. Repeat with 2 dough balls and toppings (top remaining 3 differently or freeze).
Make ahead: Form dough into balls (through step 4) and chill overnight, tightly covered with plastic wrap, instead of letting rise on counter (it will rise slowly in the fridge). You can also freeze dough for up to 2 weeks; let chilled or frozen dough come to room temperature before stretching. Make cheese topping and broccoli rabe topping up to 1 day ahead and chill, covered.
*Find at well-stocked grocery stores and Italian markets.
**While Delfina uses 3 tbsp. of kosher salt, in our tests 1 1/2 tbsp. kosher salt also delivered a well-seasoned crust. If you're concerned about sodium intake, you can successfully use the lower amount.
Note: Nutritional analysis is per slice.