1. Heat 3 tablespoons of olive oil in a large skillet over medium-high heat. Add the zucchini, eggplant and onion and sauté 3 to 4 minutes, or until fragrant and beginning to brown. Add the garlic and 1/2 cup water and season with salt and pepper. Cover and reduce the heat to medium, simmering 5 to 6 minutes or until the vegetables are just tender, stirring occasionally. Remove cover, increase the heat to medium-high and continue to cook vegetables until all the liquid has evaporated and the vegetables are sizzling.
2. Preheat the oven to broil. Spread Butter Brioche Loaf slices on a large baking sheet. Brush tomatoes on the vine with 2 teaspoons olive oil and place on baking sheet alongside the brioche slices. Broil brioche slices 1 to 2 minutes on each side, or until pale golden brown. Broil tomatoes for 4-5 minutes, or until they have shrunken and begin to burst.
3. Stir torn basil into vegetable mixture and adjust seasonings to taste. Divide vegetable mixture among the toasted brioche slices. Arrange goat cheese slices over the vegetables and broil 3 to 4 minutes, or until the cheese has begun to melt and brown. Top each tartine with the tomatoes on the vine and garnish with whole basil leaves.