Place parmesan, oil, feta brine, lemon zest, lemon juice, garlic, salt, pepper, 1 ice cube, and 2 ¼ cups beans in a food processor; process until smooth and creamy, about 2 minutes.
Transfer mixture to a shallow bowl and fold in dill, 2 ounces crumbled feta and the remaining ¾ cup beans.
Top with remaining 2 ounces crumbled feta and drizzle with more oil.
Sprinkle with more dill, lemon zest, and black pepper before serving.
Serve with crostini.
