Whisk yogurt, 2 teaspoons ginger, garlic, curry powder, cumin, and cayenne pepper in medium bowl to blend.
Add fish and turn to coat evenly. Cover and refrigerate at least 4 hours or overnight, turning fish occasionally.
Mix cucumber, vinegar, chopped cilantro, and remaining 2 teaspoons ginger in small bowl. Season lightly to taste with pepper. (Relish can be made 4 hours ahead. Cover and refrigerate, stirring occasionally.)
Prepare barbecue (medium-high heat).
Brush grill rack with olive oil. Scrape off excess yogurt marinade from fish; sprinkle fish with salt and pepper. Grill fish until just opaque in center, about 6 minutes per side.
Transfer fish to plates. Spoon cucumber relish alongside; garnish with cilantro sprigs.
*Also known as sushi vinegar; available at Asian markets and in the Asian foods section of most supermarkets.
Per serving (for halibut steaks): calories, 200; total fat, 4 g; saturated fat, 1 g; cholesterol, 64 mg; fiber, 0