Step 1

Toss chicken, garlic, ginger, lemon juice, garam masala, Kashmiri chile powder, salt, turmeric, and 1 Tbsp. oil in a medium bowl to coat. Chill 30 minutes.

Step 2

Heat remaining 1 Tbsp. oil in a large nonstick skillet over medium-high. Cook chicken until lightly browned, about 2 minutes per side (chicken won’t be cooked through). Transfer to a plate.

Step 3

Cook potatoes and carrots in a medium pot of boiling salted water until just fork-tender, 12–15 minutes. Drain and set aside.

Step 4

Heat oil in a medium Dutch oven or other heavy pot over medium-high. Add a few mustard seeds. When seeds start to wiggle and pop, reduce heat to medium and add curry leaves (if using), asafetida (if using), and remaining mustard seeds. Cover pot and cook spices, swirling, until mustard seeds start popping more gradually, about 30 seconds. Uncover pot and return heat to medium-high. Add ginger and garlic and cook, stirring constantly, until beginning to brown, about 1 minute. Add red onion and a big pinch of salt and cook, stirring often and reducing heat if needed to prevent burning, until onion is golden brown and jammy, 7–9 minutes.

Step 5

Stir in turmeric, then tomatoes and bring to a simmer. Reduce heat to medium and cook, stirring often, until tomatoes are glossy and darkened in color and oil starts to separate around edges of pot, 5–7 minutes. Add coconut milk and broth and stir to combine; season with salt. Bring curry to a simmer, then reduce heat to medium-low. Cover and cook 10 minutes, stirring occasionally to prevent sticking.

Step 6

Add chicken and reserved potatoes and carrots to curry. Return to a simmer and cook, stirring occasionally, until chicken is cooked through, 5–7 minutes. Taste and season with more salt if needed.

Step 7

Divide among bowls. Drizzle with reserved coconut milk and top with cilantro. Serve with rice.Do ahead: Curry can be made 5 days ahead; let cool. Transfer to an airtight container and chill. Curry chicken can be made 3 days ahead; transfer to an airtight container and chill.