In a large wok or skillet, drizzle vegetable oil over medium high heat. Once shimmering, add the garlic and shallots.
Cook until just aromatic, about 30 seconds. Stir in the curry powder and cook until fragrant, another minute.
Stir in the potatoes, carrots, and bell peppers. Add the water and season with salt, sugar, and black pepper.
Stir, cover, and reduce heat to medium low. Cook, stirring occasionally, until the potatoes are tender, 8-10 minutes.
If too dry and beginning to stick to pan, add a little more water. Season if needed and remove from heat. Allow to cool to room temperature or refrigerate for up to 2 days.
Preheat oven to 400˚F (205˚C) and line 1-2 baking sheets with parchment. In a small bowl, beat together the egg and milk.
On a lightly floured surface, roll out a sheet of puff pastry until it is 1/8 inch thick (3 millimeters). Cut out circles 4-5 inches (10-12 centimeters) wide using a circle cutter or small bowl.
Gather and reroll the scraps to cut out another circle or two. Repeat with remaining pastry sheet if there is one.
Place a tablespoon of the cooled filling in the center of each circle, leaving 1/2 inch (1.5 centimeter) border around the edges.
Brush the edges with the egg wash and fold the pastry over to enclose the filling in a half moon shape. Use a fork to seal the edges and transfer to prepared baking sheet. Repeat with remaining circles.
Brush the tops of the pastries with the egg wash and bake until golden brown, 15-20 minutes. Allow to cool for 5 minutes before serving.