For crostini: Preheat oven to 350°F. Combine oil, garlic and rosemary in small bowl.
Arrange baguette slices on rimmed baking sheet. Brush both sides of each slice with the herb oil mixture. Bake, flipping slices halfway through, until golden-brown, about 15 to 20 minutes. Set aside for serving with baked brie.
For baked brie: Heat oil in medium saucepan over medium heat. Add onions and cook, stirring occasionally until softened, about 3 minutes. Stir in garlic and thyme and cook until fragrant, about 30 seconds. Add vegetables in the following order: peppers, eggplant, zucchini and tomatoes. Cook each vegetable until it softens, about 2 to 3 minutes, before adding the next vegetable.
Add broth and reduce heat to medium-low. Cook, stirring occasionally, until vegetables are tender, about 5 minutes. Stir in 1 tablespoon basil and season with salt and pepper, to taste. Remove from heat and set aside for topping brie.
Line a rimmed baking sheet with parchment paper. Score a diamond pattern on top of the brie wheel with a sharp knife. Top brie with vegetable mixture and place onto prepared baking sheet. Bake until brie is melted, about 10 to 15 minutes.
Garnish with remaining basil and serve warm with crostini and crudite.