Step 1Place the bread in a bowl and add enough water to cover. Let stand at least 30 minutes to soften. Squeeze the bread dry and put it in the blender with the garlic, onion, tomatoes and the chopped fennel. Puree until smooth. Add the juice of half a lemon, the vinegar, pimenton, cumin and 1 teaspoon of salt and puree again. With the motor running, in batches if necessary, gradually add the one-fourth cup oil and the ice water. Chill well.
Step 2In a small bowl, stir together the finely diced fennel and the minced fronds. Moisten with the remaining 1 teaspoon of oil and season with a couple drops of lemon juice and a sprinkling of salt.
Step 3Before serving, stir the puree through a fine mesh strainer if you want a perfectly smooth soup. Otherwise, whisk it to gently reincorporate anything that might have separated. Taste and add more salt if necessary. Divide evenly among 4 to 6 chilled soup bowls and garnish with 1 to 2 tablespoons of the diced fennel mixture before serving.