For the stew: In a 6-quart, heavy bottomed stock pot or Dutch oven, heat 1/3 cup of oil over medium-high heat. Add the carrot, onion, and garlic. Season with salt and cook, stirring frequently, until the vegetables begin to soften, about 5 to 8 minutes. Turn the heat to high. Add the wine and scrape up the brown bits that cling to the bottom of the pan with a wooden spoon. Cook until most of the liquid has evaporated, about 5 minutes. Add the tomatoes, water and red pepper flakes. Reduce the heat and bring the mixture to a simmer. Cover and cook until the vegetables are tender, about 18 to 20 minutes. Season the fish with salt and add to the stew. Cook, stirring occasionally, until cooked through, about 5 to 8 minutes. Season the stew with salt, if needed.
For the Crostini: Put an oven rack in the center of the oven and preheat the oven to 375 degrees F.
Arrange the bread slices in a single layer on a baking sheet and drizzle with olive oil. Bake until light golden, about 12 minutes. Cool for 2 minutes. Rub the warm toasts with the cut side of the garlic.
Ladle the stew into serving bowls and garnish with parsley. Drizzle with olive oil and sprinkle a few red pepper flakes on top. Serve with the crostini.