Heat oil in a heavy bottom pan over medium heat. Add cumin seeds and let them splutter. Next, add onions, garlic, green chili, and saute until onions are soft and translucent.
Add cubed potatoes and saute for 2 minutes.
Then add 2-3 tablespoons of water, and mix well. Cover and cook the potatoes for 5 to 6 minutes or until they are fork tender but not mushy. You may stir once or twice in between.
Then add broccoli florets, along with the spices like turmeric, red chili powder, cumin powder, coriander powder, garam masala, and salt. Mix very well without burning the spices.
Cover with a lid and continue to cook for another 4 to 5 minutes (keep stirring in between), untill the broccoli is perfectly cooked. Make sure you don't overcook the broccoli.
Lastly, squeeze some lime juice. Serve Aloo Broccoli hot with bread of your choice.