1 small carrot, peeled, cut into matchstick-size strips
4 6- to 7-ounce halibut fillets
3 tablespoons vegetable oil, divided
1 shallot, thinly sliced
3/4 pound tatsoi (about 12 cups packed; baby spinach may be added if you do not have this amount of tatsoi)
Mix first 7 ingredients in medium glass bowl. Season sauce to taste with salt and pepper. (Sauce can be prepared 2 days ahead. Cover and refrigerate.) Prepare barbecue (medium-high heat). Place carrot in medium bowl. Cover with ice water. Let stand 15 minutes, then drain well. Brush fish on all sides with 2 tablespoons oil. Sprinkle with salt and pepper. Grill until just opaque in center, about 4 minutes per side. Meanwhile, heat 1 tablespoon oil in large nonstick skillet over medium heat. Add shallot; stir 1 minute. Add tatsoi; sprinkle with salt. Toss until tatsoi is wilted but still bright green, about 2 minutes; divide among 4 plates. Place fish atop tatsoi. Sprinkle each fillet with carrot; drizzle each with 2 tablespoons sauce. Serve.