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.
Next, add 2-3 tablespoons of water and mix well. Cover the pan and cook the potatoes for 5 to 6 minutes, or until they are fork-tender but not mushy. Stir occasionally to ensure even cooking.
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 cooking for another 4 to 5 minutes, stirring occasionally. Cook until the broccoli is tender yet still crunchy, making sure not to overcook it.
Lastly, squeeze some lime juice. Serve Aloo Broccoli hot with bread of your choice.