JAKARTA, Indonesia—Street food stalls known as warteg are ubiquitous in Indonesia. Hungry customers pack them during the lunch hour, lining up for fried fish or tempeh and vegetable stir-fries. They hold such a deep place in Indonesian hearts that local rappers Willy Winarko and NSG created a video in praise of warteg.

But street food has a reputation for being simple and, well, cheap — which some people in increasingly affluent Jakarta might find below their sophisticated tastes.

...