Place the frozen puff pastry sheets on a lightly floured surface and let them thaw while preparing the filling.
Blend the onion, carrot, garlic, and water in a blender or food processor until smooth.
Heat a skillet over medium heat and cook the ground meat of your choice until fully cooked.
Add the vegetable puree and cook over medium heat for 5–6 minutes, stirring occasionally, until the moisture has evaporated. The vegetables will cook as the liquid reduces.
Reduce the heat to medium-low. Add the chopped Japanese curry roux and stir until completely melted, creating a thick curry paste. Add black pepper and mix well.
Place the curry filling in the center of each puff pastry sheet. Fold each sheet into a triangle and press the edges closed with a fork.
Cut three 1-inch slits on the top of each pastry with a knife, then brush the surface with beaten egg.
Cook in the pre-heated air fryer and air fry at 350°F (180°C) for 12 minutes. Continue cooking for another few minutes, up to about 15 minutes total, until golden brown and flaky.