Warm the yogurt in the microwave for 30 seconds.
Combine the warm water, sugar, and active dry yeast in a small bowl and let it sit for 5 to 10 minutes until foamy. If it does not foam, your yeast is no longer active and you should start over with a fresh packet.
In the bowl of your stand mixer fitted with the dough hook, combine the bread flour and salt and mix briefly on low to distribute. In a separate bowl whisk together the Greek yogurt, the bloomed yeast mixture, and the olive oil until smooth, then pour the wet ingredients into the flour.
Mix on low speed until a shaggy dough forms, about 2 minutes, then increase to medium speed and knead for 6 to 8 minutes until the dough is smooth, pulls away cleanly from the sides of the bowl, it may stick to the bottom a little. Because this is an enriched dough you are looking for dough that stretches without immediately tearing. It should feel tacky but not sticky. It will not behave the same way as a traditonal pizza dough.
Transfer the dough to a lightly oiled bowl, cover, and rise at room temperature for 1 to 1.5 hours until visibly puffy and increased in size. You do not need it to fully double.
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 generously, 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. Keep the filling pulled in slightly from the edges of each well so the cheese does not run up the sides.
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.
Bake at 425 degrees F for 18 to 22 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.
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.