Combine flour, salt, yeast, 2 egg yolks, oil, and water in a large mixing bowl. Mix the ingredients and knead the dough until it has reached a springy consistency. Let rise at room temperature (or someplace warm) for 2 hours.
Divide the dough into 12 equal portions. Set aside about a fifth of each portion and roll the remaining dough into a ball. Roll out with a rolling pin and place about a third of a hot dog or one little smokie in the center, cover with cheese, and fold the dough back together, forming it once again into a ball. Use the side where the ingredients are sealed in as the bottom of the pig. Brush the upper ball with beaten egg. With the leftover fifth of dough, form a small circle as the pig's snout and insert two food-safe wooden sticks as the nostrils, using the sticks to affix the snout to the front of the pig. Form a second circle and cut it in half, rolling each together to form ears. Press these to each side of the pig's head. Place two peppercorns as the eyes. Now make the tail by rolling the dough into a curly rope and attach at the rear.
Bake at 350 °F for 17 minutes, leaving the wooden sticks in place so the nostrils don't bake together. When the pigs have been removed from the oven, you can remove the sticks.
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