Start by chopping your broccoli into bite-sized pieces and peeling and cubing the potatoes into about 2 cm chunks. Mince the garlic and grate the ginger, setting everything aside.
Heat the oil in a large skillet or wok over medium heat until it shimmers and begins to ripple. Add the minced garlic and grated ginger, cooking for about 30 seconds until fragrant and slightly golden, filling the kitchen with a warm aroma.
Stir in the turmeric, cumin, and coriander, cooking briefly for about 20 seconds until the spices toast slightly and release their fragrant oils. Be careful not to burn them; adjust the heat if needed.
Add the cubed potatoes to the skillet, stirring well to coat them evenly with the spices. Cook for about 5 minutes, allowing the edges to turn a light golden brown and smell warm and nutty.
Pour in the coconut milk, stirring to combine everything. Bring the mixture to a gentle simmer, then cover the skillet and reduce the heat to low. Let the potatoes cook for about 10 minutes, stirring occasionally, until they are tender and the sauce has thickened slightly.
Add the broccoli florets to the skillet, stirring to distribute them evenly in the curry. Cover again and cook for another 5-7 minutes, until the broccoli turns bright green and is just tender but still slightly crisp.
Uncover the skillet, taste the curry, and season with salt as needed. Squeeze in a bit of lemon or lime juice to brighten the flavors. Cook for another 2 minutes uncovered to allow the sauce to thicken just a little more.
Remove from heat and let the curry sit for a couple of minutes so the flavors settle. Serve hot, garnished with fresh herbs if desired, alongside rice or flatbread for a complete meal.
