1. Heat oil in a small frying pan over medium-high heat. Add panch phoron and cook, stirring, until seeds begin to pop, about 30 seconds. Reduce heat to medium. All at once, add bay leaves, ginger, and garlic; cook, stirring, until ginger softens, about 3 minutes. Remove from heat, stir in coriander and salt, and let stand until fragrant, about 30 seconds. Add yogurt, stir to loosen browned bits, and let marinade cool.
2. Marinate by putting chicken, bell peppers, and carrots in a 1-gal. resealable plastic bag. Scrape in yogurt mixture, seal, and squish to coat. Chill at least 2 hours or overnight.
3. Bake chicken: Preheat oven to 475° with a rack set in upper third of oven. Put potatoes on a large rimmed baking sheet and squeeze contents of bag over them. Mix to coat, then pat ingredients into a single layer. Bake, turning food with a wide spatula every 15 to 20 minutes and ending with chicken skin side up, until browned, 40 to 45 minutes.