Heat vegetable oil in a large skillet over medium heat; add cumin seeds. Cook until seeds begin to pop and crackle, 1 to 2 minutes. Cook and stir onion and garlic into cumin seeds until onions are slightly softened, about 5 minutes. Add turmeric and chili powder; stir to coat. Stir in tomato puree until fully incorporated, 1 to 2 minutes.
Cook and stir chicken, carrots, potatoes, and green beans into onion mixture. Season with salt. Cover the skillet with a lid and lower heat to medium-low. Simmer, stirring occasionally, until vegetables are about half cooked, about 10 minutes.
Whisk water and coconut cream together in a bowl; pour into chicken and vegetable mixture. Cover skillet and simmer until chicken is fully cooked and no longer pink in the center and vegetables are tender, 5 to 10 more minutes.
