1. Preheat the oven to 350°. In a large, heavy pot, heat 2 tablespoons of the olive oil. Add the leeks and garlic and cook over moderate heat until softened, about 5 minutes. Add the large cauliflower florets and the apple and cook, stirring, for 2 minutes. Add the broth and thyme sprigs and bring to a boil. Cover and simmer over low heat for 45 minutes.
2. Spread the diced rye bread, pecan pieces and tiny cauliflower florets on a large rimmed baking sheet. Drizzle with the remaining 1 tablespoon of olive oil and toss to coat. Season generously with salt and pepper and bake, stirring once, for about 10 minutes, or until the rye bread croutons are crisp.
3. Discard the thyme sprigs from the soup. Working in batches, puree the soup in a blender. Return the soup to the pot and season with salt and pepper. Ladle into bowls, scatter the croutons, pecans and cauliflower on top and serve.
4. MAKE AHEAD The soup can be refrigerated overnight. Reheat gently before serving. Add more chicken broth to thin the soup to the desired consistency, if needed.