Add flour, curry powder, and salt to a food processor. Pulse until combined. Add shortening and cold butter, pulse until mixture resembles coarse crumbs. Gradually add ice water until mixture comes together. Wrap in plastic and chill.

Melt butter in a cast-iron skillet over medium-high heat. Add chicken, onion, celery, carrots, and curry powder; cook until onion softens and chicken is cooked thoroughly.

Add flour to the skillet and cook for 3 minutes. Slowly stir in broth and yogurt, simmer until the mixture thickens.

Remove skillet from heat. Stir in cilantro, salt, pepper, and thyme.

Preheat oven to 400°F (200°C). Roll out chilled dough to 1/8-inch thickness. Cut shapes using cookie cutters.

Arrange dough shapes on top of the filling, overlapping as needed. Brush egg over the dough.