Pulse together coconut milk, the lemongrass, shallot, 2 tablespoons juice, the fish sauce, 2 teaspoons brown sugar, the garlic, salt, cumin, and turmeric in a food processor until smooth. Divide mixture between 2 resealable plastic bags, place steak in one and chicken in the other, then seal bags and turn until meat is coated well. Marinate, chilled, at least 4 hours or overnight, placing bags in large bowls to catch any leaks.

Heat oil in a small heavy saucepan over moderate heat. Add curry paste and remaining 1 tablespoon brown sugar; cook, stirring, until sugar dissolves, about 2 minutes. Remove pan from heat and whisk in remaining 3/4 cup coconut milk, the peanuts, cilantro, and remaining 2 tablespoons juice (or to taste), for peanut dipping sauce.

Remove steak and chicken from marinade (discard marinade) and thread on drained skewers.

Preheat grill and lightly oil rack. Combine vinegar and granulated sugar in a small saucepan; bring to a simmer. Cook, stirring, until sugar dissolves, about 2 minutes, for basting sauce.

Grill meat, brushing both sides with basting sauce during last minute of cooking, turning once, until chicken is cooked through, about 4 minutes, and steak, turning once, about 2 minutes for medium-rare (discard remaining basting sauce). Arrange skewers on a platter and serve with peanut dipping sauce. Makes 8 servings.