Preheat the oven to 425 degrees F. Combine the turnip and carrot in a large microwave-safe bowl with 1 tablespoon water. Cover with plastic wrap and microwave until just softened, 3 to 5 minutes. Drain.
Add the beef curry and Worcestershire sauce to the vegetables and stir to combine; season with salt and pepper. Unroll the pie dough and cut each round in half. Spoon one-quarter of the filling on one side of each semicircle and fold in half to form a wedge. Crimp the edges with a fork to seal. Transfer to a baking sheet; cut two or three slits in the tops. Bake until deep golden brown, about 20 minutes.
Meanwhile, combine the shallot with 2 tablespoons each vinegar and water in a small bowl; let stand 10 minutes, then drain. Whisk the remaining 1 tablespoon vinegar, the olive oil and mustard in a large bowl until smooth; season with salt and pepper. Add the arugula, parsley and shallot and toss. Serve with the handpies and more mustard for dipping.
Slow-Cooker Beef Curry:
Yield:Photograph by Antonis Achilleos
Toss the beef and potatoes with the curry powder, 1 teaspoon cumin, 1 tablespoon ginger, the garlic, 1 teaspoon salt and a few grinds of pepper in a 6-quart slow cooker. Crumble 1/2 slice of naan into small pieces over the beef and potatoes, then pour in the tomatoes. Cover and cook on low, 7 hours.
Uncover and skim off any fat from the top of the mixture. Stir well to combine, then let stand 10 minutes. Meanwhile, combine the cilantro, pickled jalapenos and brine, 1/4 cup water and the remaining 1/4 teaspoon cumin and 1 tablespoon ginger in a food processor. Pulse until combined; season with salt and pepper.
Stir 3 tablespoons of the cilantro puree into the slow cooker; season with salt and pepper. Serve the curry with the naan; top with the remaining cilantro puree.