Heat 1 tablespoon oil in a large skillet over medium-high heat. Add zucchini, fennel, and half of onions; cook 3 minutes or until tender. Stir in thyme, 2 tablespoons capers, rind, salt, and pepper.
Heat remaining 3 tablespoons oil in a large cast-iron skillet over medium-high heat. Add roasted potatoes; cook 4 minutes or until golden brown. Stir in zucchini mixture and roasted garlic cream. Cook 1 minute.
Stir in half-and-half to loosen hash. Divide hash among 6 plates. Top each serving with 1 1/3 ounces trout. Sprinkle evenly with remaining onion, remaining 1 tablespoon capers, and chives. Serve with lemon wedges.