Heat the oil in a large pot over medium heat until it shimmers and starts to gently sizzle.
Add the sliced leeks to the pot and cook, stirring often, until they soften and become fragrant, about 8 minutes. They should turn tender and slightly translucent, filling your kitchen with a mild onion aroma.
While the leeks cook, peel and dice the potatoes into 1-2 cm cubes, ready to add later.
Sprinkle the cumin seeds into the pot with the leeks, and toast for about 30 seconds until they become fragrant and slightly darker, releasing their aroma.
Add the turmeric and coriander powder to the pot, stirring quickly for about 15 seconds until the spices are fragrant and well mixed with the leeks and cumin.
Pour in the coconut milk and vegetable broth, stirring gently to combine everything. Bring the mixture to a gentle simmer, watching for bubbles to form slowly around the edges.
Add the diced potatoes to the simmering broth. Cover loosely and cook on low heat for about 20 minutes, stirring occasionally, until the potatoes are tender and easily pierced with a fork.
Check the texture; the curry should be slightly thickened and aromatic. If it’s too thin, simmer uncovered for a few more minutes to allow it to reduce slightly.
Use an immersion blender to blend part of the curry directly in the pot, or mash some of the potatoes with a fork to create a velvety, slightly chunky texture—this enhances creaminess.
Season the curry with salt and pepper to taste. Squeeze in the fresh lemon juice, stirring to brighten the flavors.
Turn off the heat, then sprinkle chopped cilantro over the top for a fresh, herbal finish. Let the curry rest for about 5 minutes to allow flavors to meld.
Serve the warm, velvety leek and potato curry in bowls, garnished with extra cilantro or a drizzle of olive oil if desired. Enjoy the comforting aroma and rich, earthy flavors.