Combine the yogurt, ginger, garlic, and curry powder in a shallow mixing bowl, stir to combine. Place the chicken strips in the yogurt marinade and gently toss until well coated. Cover and let the chicken marinate in the refrigerator for at up to 2 hours.
Thread the chicken pieces onto the soaked skewers working the skewer in and out of the meat, down the middle of the piece, so that it stays in place during grilling. Place a grill pan over medium heat and brush it with oil to prevent the meat from sticking. Grill the chicken satays for 3 to 5 minutes on each side, until nicely seared and cooked through. Serve the satays on a platter lined with lettuce leaves and cilantro; accompanied by a small bowl of peanut sauce on the side.
Combine the peanut butter, soy sauce, red chili paste, brown sugar, and lime juice in a food processor or blender. Puree to combine. While the motor is running, drizzle in the hot water to thin out the sauce, you may not need all of it. Pour the sauce into a nice serving bowl and garnish with the chopped peanuts. Serve with chicken satay.