To begin, mix yeast, sugar, and warm water in a large bowl. Allow to bloom for 10 minutes until foamy. Add flour, salt, and oil, then knead into a soft dough for 8–10 minutes. Cover and let rise until doubled in size, around 1 hour. Move to shaping.
Punch down the dough and divide into 4 pieces. Shape each into a ball, then flatten slightly to a round of about 15 cm. Place on a baking tray lined with parchment. Rest for 15 minutes while preheating the oven.
Preheat the oven to 220°C. Bake for 12–15 minutes until puffed and golden. Remove from oven and allow to cool slightly before cutting. Continue to prepare the filling.
Pour the lamb stock into a saucepan and warm gently over low heat. The stock should be hot but not boiling to soak the bread without turning it soggy too quickly. Transition to preparing bread for filling.
Slice the top off each lepinja and gently hollow out some of the crumb. Keep the top as a lid. This creates space for the filling. Move to assembling.
Into each hollowed bread, place an egg yolk, a generous spoonful of kaymak, and a small pinch of salt. Pour hot stock inside, allowing the bread to absorb the liquid. Replace the bread lid. Transition to finishing.
Return the stuffed breads to the oven for 3–4 minutes until the yolk warms and the filling melds. Avoid over baking to maintain a runny yolk. Proceed to final presentation.
Serve Komplet Lepinja immediately with extra kaymak on the side. Garnish lightly with parsley if desired. Presentation tip: cut in half and serve on wooden boards to echo its rustic origins.