In a 12-inch sauté pan or skillet, heat olive oil over medium-high heat until hot. Reduce heat to medium and add tuna steaks. Cook until crumbs turn golden brown, about 2 minutes. Carefully turn steaks and cook 2 minutes for rare or 3 minutes for medium-rare. Move tuna to a plate and cover loosely with foil to keep warm.
Add zucchini to same pan and increase heat to high. Cook, stirring, 1 minute, or until wilted. Add carrot and cook, stirring, 2 minutes, or until vegetables are tender-crisp. Stir in shallot, olives, thyme, gin and vermouth, and cook 1 minute. Add stock and bring to a boil; let boil 1 minute or until reduced slightly. Stir in butter and salt. Remove pan from heat; discard thyme.
To serve, cut each tuna steak in half. Arrange sautéed vegetables in the center of 4 plates and stack 2 tuna halves on top of each; drizzle with sauce.