Heat the vegetable oil in a large deep pan over medium heat until it shimmers and begins to gently crackle.
Add the chopped onion and cook, stirring occasionally, until it turns translucent and starts to brown slightly, about 5 minutes. The aroma should be sweet and inviting.
Stir in the cumin seeds, turmeric, and chili powder, cooking for about 30 seconds until fragrant and slightly smoky, watching for a gentle sizzle.
Add the minced garlic and grated ginger, cooking for another minute until fragrant and the mixture turns golden, filling the air with a warm aroma.
Stir in the diced potatoes, coating them with the spice mixture, and cook for 5 minutes, stirring occasionally, until they start to turn golden on the edges.
Pour in the coconut milk and water, stirring well, then bring to a gentle simmer. Cover the pan and cook for about 10 minutes, until the potatoes are tender and the sauce begins to thicken.
Add the broccoli florets and stir to combine. Cover again and cook for 8-10 minutes, until the broccoli is vibrant green and just tender but still slightly crisp.
Uncover and simmer for another 2 minutes to let the sauce thicken slightly, stirring gently. Taste and season with salt and a squeeze of lemon juice for brightness.
Remove from heat and let rest for a few minutes to meld the flavors. Serve hot with rice or bread, garnished with fresh herbs if desired.