Preheat oven to 350℉.
Heat 1 tbsp olive oil in a Dutch oven over medium heat. Pat chicken thighs dry with a paper towel and season on all sides with a generous sprinkle of salt and pepper. Place skin-side down in the pot and cook for about 5 minutes, or until skin is golden brown. Remove to a plate.
Without wiping out the pan, add onion, garlic, ginger, turmeric, cumin seeds, ½ tsp salt, and ¼ tsp pepper. Cook briefly until fragrant and onion is starting to soften, about 1-2 minutes.
Add greens and cook while stirring until wilted. Mix in canned tomatoes with their juices.
Return chicken to pot skin-side up on top of greens. Cover, remove from heat, and transfer to the oven. Cook for about 45 minutes or unti chicken is very tender and easy to shred with a fork.
About halfway through, start cooking rice: combine 1 cup rice and 2 cups broth or water in a medium saucepan. Bring to a gentle boil then cover and reduce heat to low. Simmer for 15 minutes then remove heat and leave covered until ready to serve.
Remove chicken to a cutting board. Transfer remaining contents from the pot to a blender. Add yogurt and blend until fairly smooth.
Return sauce to pot over low heat. Remove skin and bones from chicken thighs and shred meat with two forks. Mix into the green sauce.
Divide rice into bowls. Ladle chicken and green sauce over rice then top with goat cheese. Sprinkle chili powder over the top.