For the dough: Whisk together the warm water, yeast and 1 teaspoon of the sugar in a bowl. Set aside until the yeast activates and becomes foamy on top, about 10 minutes.
Heat the milk and butter in a small pot until the butter melts. Allow to cool to less than 115 degrees F.
Whisk the flour, salt and remaining sugar in the bowl of a stand mixer fitted with a dough hook. Add the foamy yeast mixture and cooled milk and butter. Turn on the mixer to knead the dough for about 5 minutes. The dough should be a smooth uniform ball that no longer sticks to the sides of the bowl. Cover the bowl with plastic wrap and put in a warm area until the dough doubles in size, about 1 1/2 hours.
For the filling: In the meantime, heat 1 tablespoon vegetable oil over high heat in a large skillet. Add the ground beef and sprinkle with 1 1/2 teaspoons salt. Brown the beef, breaking it up into small pieces, about 5 minutes. Once browned, transfer the beef to a bowl and add the remaining 2 tablespoons of oil to the skillet. Reduce the heat to medium, add the cabbage and onions, season with the remaining 1 teaspoon salt and cook until soft, about 15 minutes. Add the browned beef back to the skillet and continue cooking an additional 5 minutes with the cabbage and onions. Season with the white pepper and additional salt if needed. Take off the heat and set aside to cool completely.
Preheat the oven to 350 degrees F. When the dough has doubled in size, punch it down and divide it into 10 equal-size balls, about 3 1/2 ounces each. Roll out each ball one at a time into a rectangle, roughly 6 by 8 inches. Spread 1/2 cup cooled filling in the center of the rectangle. Bring the two long sides of dough together so the seam is facing up and pinch them together. Pinch the short ends shut as well. You should have a rectangular shape. Put the filled dough seam-side down on a parchment-lined baking sheet. Repeat with the remaining 9 balls. You will need 2 baking sheets to fit all 10 meat pies. Cover the meat pies with a dish towel and allow them to rest for about 20 minutes. Bake in the oven until golden brown, 20 to 25 minutes.
Melt the butter. As soon as the meat pies come out of the oven, brush the tops with the melted butter. Serve with ketchup.
Cook's Note: After they have baked and cooled you can freeze up to a month. To reheat, take right out of the freezer, cover with foil and place into a 350 degree oven until heated through, 20 to 25 minutes.