Stir together mascarpone cheese, olive oil, green onion, lemon zest, and 2 tablespoons each parsley and dill in a medium bowl until blended. Flake tuna into mixture, and gently stir to combine. Stir in salt and pepper. Cover and chill at least 2 hours or up to 1 day.
Transfer rillettes to a serving dish, and sprinkle with remaining 1 tablespoon each parsley and dill. Serve with crostini or crackers.