1. Heat a Dutch oven over medium heat. Add 1 tablespoon oil; swirl to coat. Add fennel, onion, garlic, and 1/4 teaspoon salt; cook 1 minute. Reduce heat to medium-low, cover, and cook 6 minutes or until crisp-tender (do not brown), stirring occasionally.
2. Add remaining 1/4 teaspoon salt, 2 1/2 cups water, vinegar, and beans. Bring to a boil; cover, reduce heat, and simmer 10 minutes. Place half of mixture in a blender. Remove center piece of blender lid (to allow steam to escape); secure blender lid on blender. Place a clean towel over opening in blender lid (to avoid splatters). Blend until smooth. Pour into a large bowl. Repeat procedure with remaining mixture.
3. Combine almonds, mint, rind, and cheese. Divide soup among 4 bowls; top with almond mixture. Drizzle with remaining 2 teaspoons oil.
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