Process beans, garlic, basil leaves, olive oil, 1 Tbsp. fresh lemon juice, and kosher salt in a food processor until smooth, stopping to scrape bowl as needed. Cover and chill until ready to assemble.
LAYERS 2, 3 & 4
Rinse onion in cold water, and pat dry. Cut grape tomatoes into halves. Stir together pickled okra and sliced olives.
Stir together sour cream, parsley, mint, lemon zest, 1 Tbsp. lemon juice, and ground cumin in a medium bowl. Cover and chill until ready to assemble.
Stir together black-eyed peas, chopped bell pepper, minced jalapeño pepper, hot sauce, and freshly ground black pepper. Cover and chill until ready to assemble.
ASSEMBLY Layer bean mixture; minced onion, tomatoes, pickled okra mixture; sour cream mixture, black-eyed pea mixture, and feta cheese in an 11- x 7-inch baking dish. Cover and chill 1 to 2 hours before serving. Serve with pita or multigrain chips and crudités.