The small bits of cauliflower gives the chowder broth a nice clean thickness.
Remove leaves from cauliflower and cut head in half. Coarsely chop 1 half, then pulse in a food processor until a fine crumble forms. Break remaining cauliflower into small florets.
Heat 1/4 cup oil in a medium pot over medium-high. Cook leeks, tossing often, until softened, about 5 minutes; season with salt and pepper. Mix in garlic and all of the cauliflower. Add tomatoes and broth and use a wooden spoon to crush some of the tomatoes. Bring mixture to a simmer, then add monkfish, olives, and tarragon; season with salt and pepper. Return to a simmer; cover pot and cook, stirring often, until flavors soften and blend together, about 20 minutes. Season with more salt and pepper if needed.
Ladle chowder into bowls, drizzle with more oil, and grind some pepper over. Serve with bread for dunking.