Warm your yogurt in the microwave for 30 seconds.
In the bowl of your stand mixer fitted with the dough hook, combine the bread flour, salt, and sugar and mix briefly on low to distribute. In a separate bowl whisk together the Greek yogurt, sourdough starter, water, and olive oil until smooth, then pour the wet ingredients into the flour.
Mix on low speed until a shaggy dough forms, about 2 minutes, cover and let rest about 30 minutes. This dough hydrates differently than a regular pizza dough.
Knead on medium speed for 5-6 minutes until the dough is smoother, pulls away cleanly from the sides of the bowl. You are looking for dough that stretches without immediately tearing. It should feel tacky but not sticky.
Transfer the dough to a lightly oiled bowl, cover, and rest for 1 hour.
Do one set of stretch and folds, working around the bowl and pulling the dough up and over itself four times. Cover again.
Bulk ferment at room temperature for 6 to 8 hours, until the dough has risen noticeably and looks puffy and alive. Go by the look of the dough rather than the clock, since kitchen temperature changes everything.
At this point you can shape immediately, or cover the bowl tightly and cold ferment in the refrigerator overnight for deeper flavor. If the dough has been refrigerated, pull it out and let it rest at room temperature for 30 to 45 minutes before rolling. Cold dough will tear instead of stretching.
Remove the sausage from its casings if you are using links, then brown it in a skillet over medium heat, breaking it into small crumbles as it cooks. Drain thoroughly on paper towels if you are using pork.
Butter the wells of the hot dog bun pan, taking the butter all the way up the sides to the rim. If you used a lean chicken sausage, butter the bottoms of the wells as well.
Divide the mini pepperoni and the cooked sausage evenly among the ten wells, pushing everything all the way into the corners so the end sticks are not left bare.
Pipe about half the pizza sauce over the meat, scatter the mozzarella evenly over the top, then pipe the remaining sauce over the cheese.
Preheat your oven to 425 degrees F.
On a lightly floured surface, roll the dough into a rectangle about 15 by 6 inches, matching the baking surface of the pan. Lay it over the filled pan in one motion and leave it where it lands. Do not slide or press it around, which drags the filling out of position. Ease the edges gently into the corners with your fingertips.
Dock the dough all over with a fork, the same way you would dock a pizza crust. This keeps large bubbles from lifting the dough away from the filling underneath. Gently push the dough down into the fillings, too hard and it will squish out.
Bake at 425 degrees F for 18 to 25 minutes, until the top is firm with no give in the center and the internal temperature reads around 190 degrees F. Start checking at 18 minutes if your oven runs hot, since the cheese is against the hot metal on the bottom where you cannot see it. You should be able to watch the edges.
Let the pan rest on a wire rack for 5 minutes, then invert onto the rack so the filling side faces up. Cool for another 10 minutes before slicing.
Slice down the ridge lines the pan pressed into the bread to get ten even sticks. Serve warm with extra pizza sauce for dipping.