Soak the bamboo or wooden skewers in water for 30 to 60 minutes.
With a sharp knife, cut each chicken breast lengthwise into 12 long, thin strips. Thread 1 strip onto each of the skewers, weaving the skewer back and forth along the length of each chicken strip. Arrange them on a large platter or baking tray.
To prepare the marinade, in a small bowl combine the curry powder, pepper, salt and cumin. Spoon the oil over the chicken strips, turning to coat them evenly, and then evenly sprinkle the dry ingredients over them on both sides. Cover the platter or tray with plastic wrap and marinate in the refrigerator for 1 hour or longer.
To prepare the mint-soy vinaigrette, in a food processor fitted with the steel blade or a blender, combine the egg yolks, vinegar, mint, soy sauce and coriander. With the motor running, slowly drizzle in the oil and continue processing until smooth. Transfer the dressing to a bowl, season to taste with salt and pepper, cover with plastic wrap and refrigerate until ready to serve.
Preheat a hinged indoor grill or panini maker, according to the manufacturer's instructions, or preheat a broiler, outdoor grill, or stovetop grill pan. Grill the skewers, in batches if necessary, until cooked through and nicely browned, about 2 minutes total on a hinged grill or panini maker or 2 minutes per side in the broiler, in a grill pan, or on an outdoor grill. If using an indoor grill, take care that the skewers don't prevent the grill or panini maker from closing properly.
Serve the skewers immediately, passing the vinaigrette for guests to drizzle over their own skewers or to use as a dip.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.