Prepare the Dough: In a small bowl, dissolve the fresh yeast and 1 tablespoon of sugar in the warm water. Let it sit for about 5-10 minutes until a foamy layer forms on top. In a large mixing bowl, combine the flour, salt, and the remaining 1 tablespoon of sugar. Add the yeast mixture, warm milk, vegetable oil, egg, and egg yolk. Knead the dough for 10-15 minutes by hand or with a stand mixer on medium speed until it is smooth and elastic. Add the softened butter and continue kneading until it is fully incorporated. Place the dough in a lightly oiled bowl, cover it with a clean towel, and let it rise in a warm, draft-free place for 50-60 minutes, or until it has roughly doubled in size.

Make the Filling: While the dough is rising, prepare the red currant filling. In a small saucepan, combine the red currants, sugar, cornstarch, vanilla sugar, and lemon juice. Cook over medium heat for 5-7 minutes, stirring constantly, until the mixture thickens into a jam-like consistency. The cornstarch will help it thicken as it cools. Remove from the heat and let the filling cool completely.

Assemble the Buns: Once the dough has risen, gently punch it down to release the air. Transfer the dough to a lightly floured surface and divide it into 10-12 equal pieces. Roll each piece into a flat circle. Place a spoonful of the cooled filling in the center of each circle. Fold the edges of the dough over the filling and pinch them together tightly to seal. Place the buns on a parchment-lined baking sheet, seam-side down.

Final Rise and Bake: Preheat your oven to 180 °C (356 °F). Cover the buns with a clean towel and let them rise for a second time for about 20-30 minutes. In a small bowl, whisk the egg and milk together to create an egg wash. Brush the tops of the buns with the egg wash. Bake for 30-35 minutes, or until they are golden brown and cooked through.

Make the Glaze: While the buns are cooling, whisk together the powdered sugar, sour cream, and vanilla extract until a smooth, pourable glaze forms.

Cool and Serve: Allow the buns to cool on a wire rack for a few minutes before drizzling the glaze generously over the tops. Serve warm or at room temperature to enjoy the beautiful contrast of flavors.