Place 1 3/4 cups flour into a bowl. Stir in sugar, yeast, and salt.

Combine milk, water, and shortening in a microwave-safe bowl. Heat on high until warm (120 to 130 degrees F/50 to 55 degrees C), 2 to 3 minutes.

Pour heated milk into the flour mixture. Add eggs and beat at low speed for 30 seconds. Switch to high speed and beat for 3 minutes. Stir in the remaining flour. Knead until smooth, about 3 minutes. Cover the bowl with waxed paper and a towel; let rest for 20 minutes.

Cook ground beef and onion in a nonstick skillet over medium-high heat until beef is browned, 5 to 7 minutes.

At the same time, melt butter in a separate skillet over medium heat. Add cabbage and cook until wilted, about 5 minutes. Add cabbage to beef mixture with salt and pepper. Remove from the heat.

Preheat the oven to 350 degrees F (175 degrees C). Grease a large baking sheet.

Roll dough on a lightly floured surface until very thin. Cut into 6 squares or rectangles, whichever you prefer. Place 3 tablespoons beef filling in the center of each shape. Bring corners together, pinch edges to seal, and place right-side up onto the prepared baking sheet. Let rise until an indentation remains when lightly pressed with a finger, 40 to 60 minutes.

Bake in the preheated oven until dough is done and golden brown, about 20 minutes.