Place bitter gourd rings in a microwave-safe bowl. Toss with 1 teaspoon oil and salt to coat. Microwave, stirring halfway through, until tender, about 4 minutes.
Heat the remaining oil in a saucepan over low heat. Add the gourds and asafoetida powder. Cook and stir until slightly browned, about 10 minutes. Add besan, ground red chile, and coriander; cook and stir until flavors meld, about 3 minutes. Add jaggery; mix well.
