Process beans, garlic, lemon juice, and 1 teaspoon each of the lemon zest and salt in a food processor until smooth and thick, about 1 minute. Remove from food processor and set aside. Wipe food processor bowl clean.
Place pistachios, parsley, mint, red pepper, and remaining 1 teaspoon lemon zest in food processor and pulse until coarsely chopped, 6 to 7 times. Transfer to a bowl. Stir in oil and remaining 1/2 teaspoon salt.
Spread bean mixture on 1 side of each bread half. Slightly overlap 4 halves on each of 6 plates. Top each plate with 2 tablespoons pistachio mixture and sprinkle evenly with cheese.