Place cabbage, celery, dill, and cilantro in a large stockpot. Pour in enough water to barely cover. Bring to a boil; cook uncovered until cabbage and celery are just tender, about 10 minutes. Add banana peppers. Stir in spinach bit by bit, waiting for it to wilt between batches. Reduce heat to medium-low.
Whisk yogurt and flour in a bowl. Add to the stockpot. Season with lemon juice and salt. Cook, stirring constantly, until yogurt is hot but not boiling, 7 to 10 minutes.