Combine the soy sauce, mirin, sugar, ginger and garlic in a medium saucepan. Bring to a boil, reduce the heat and simmer until the mixture forms a sticky glaze, 15 to 20 minutes.
Preheat a grill to medium-high heat. Brush the salmon with the glaze and grill to desired doneness, basting frequently. Let cool, then flake.
To assemble the shiso wraps, place some sushi rice on a shiso leaf and top with the salmon. Drizzle with the teriyaki sauce and garnish with some wasabi peas and daikon sprouts.