Shred zucchini using the wide holes of a box grater. Squeeze dry in a clean kitchen towel. Add zucchini, 2 tablespoons oil, and garlic to a large, deep skillet over medium-low heat; cook 15 minutes, stirring occasionally. Add 2 tablespoons water during last 2 minutes of cooking, scraping pan to loosen browned bits. Cool.
Combine parsley, almonds, and mint in a food processor; pulse until finely chopped. Add zucchini mixture, remaining 2 teaspoons oil, rind, juice, salt, and pepper; pulse until combined but not smooth. Stir in cheese.
Cook beans in boiling water 3 to 4 minutes; drain and rinse with cold water. Serve dip with green beans, tomatoes, and bell peppers.