Warm about 1 cup of Milk to lukewarm (about 38–43°C / 100–110°F), stir in 1 tsp of Sugar and 2 tsp of Instant Dry Yeast; let sit 5–10 minutes until foamy.
In a large bowl whisk together 3 1/2–4 cups of All-Purpose Flour and 1 tsp of Salt. Make a well in the center.
Pour the yeast mixture into the flour, add one beaten Egg and 3 tbsp melted and cooled Unsalted Butter. Stir until a shaggy dough forms.
Turn the dough onto a lightly floured surface and knead 8–10 minutes until smooth and elastic (add a little flour if very sticky). Place in a lightly oiled bowl, cover, and let rise in a warm place until doubled, about 1–1.5 hours.
While the dough rises, prepare the filling: thinly shred about half a head of White Cabbage, finely chop one Onion and grate one medium Carrot.
In a large skillet heat 1–2 tbsp Sunflower Oil and 1 tbsp Unsalted Butter over medium heat. Add the Onion and Carrot and cook until softened, 4–5 minutes, then add the White Cabbage and cook until tender and any excess moisture has evaporated, about 8–10 minutes.
Season the cooked vegetables with 1 tsp Salt, 1/2 tsp Black Pepper and 1–2 tbsp chopped Dill. Taste and adjust seasoning, then cool the filling to room temperature.
Punch down the risen dough and divide into 12–16 equal pieces. Flatten each piece into a 3–4 inch disk, place about 1–2 tablespoons of the cooled filling in the center, and pinch the edges to seal into an oval or round bun.
Place the filled pirozhki seam-side down on a baking sheet lined with parchment. Whisk one more Egg with a splash of Milk and brush the tops for a glossy finish.
Bake in a preheated oven at 375°F (190°C) for 18–25 minutes, or until golden brown. Cool slightly before serving — best warm.
