Dough: Place the butter and water in a medium-sized saucepan, and heat gently, stirring occasionally, until the butter melts then bring the mixture to a rolling boil.
Meanwhile, sift the flour, turmeric, cayenne pepper, and salt into a large bowl. Make a well in the middle of the flour, and add the egg.
Pour the hot liquid into the flour and stir with a wooden spoon to mix.
Spread the mixture out on a large plate with the wooden spoon and cool, about 15 minutes. Then wrap in plastic wrap, and place in the refrigerator for 30 minutes, or until firm.
While the dough is chilling, heat the olive oil in a saucepan set over a medium heat. Add the onions, garlic, ginger, and season with salt and pepper. Cook the mixture until the onions are soft and slightly golden.
Grind the seeds in a mortar with a pestle, and then add to the pan with the beef, tomato puree, garam masala, mustard and Worcestershire sauce. Cook over medium heat, until the beef is cooked, about 15 minutes. Add the peas for the last 1 to 2 minutes of cooking. Add the chopped mint, then season with salt and pepper to taste, and allow to cool.
When ready to assemble, preheat the oven to 425 degrees F. Roll the pastry dough out on a lightly-floured work surface until it is approximately 1/16-inch thick. Using a small cup saucer or biscuit cutter, cut the dough into 12 1/2-inch circles.
Lay 1 generous tablespoon of the mixture on one half of the circle, and brush the edge of the other half with the beaten egg, and then fold it over to form a semi-circle. Pinch the edges together to seal, making sure there is no air trapped inside, and mark or score the edges with a fork. Repeat until all the circles and filling are used up.
Brush the tops with beaten egg, and bake in the oven until golden and a skewer inserted in the center of one comes out hot, about 15 to 20 minutes. Serve the pasties hot or at room temperature.