For the sauce: Heat the oil in a pot, and then add the garlic and onions. Cook until the onions are translucent and the garlic is lightly browned around the edges, about 12 minutes. Add the basil, parsley, thyme and carrots and cook for 5 to 8 minutes. Pour in the crushed tomatoes and sprinkle with salt and pepper. Bring to a boil, and then reduce to a simmer and cook for about 30 more minutes, stirring often.
For the crostini: Preheat the oven to 375 degrees F. Spray a baking sheet with olive oil spray. Add the baguette slices and bake until golden brown, 8 to 10 minutes. Serve the marinara with braciole and crostini.