Peel and dice the potatoes into roughly 1-inch chunks, then set aside. Slice the leeks thinly, rinsing thoroughly to remove any dirt trapped between layers.
Heat the oil in a large heavy-bottomed pan over medium heat until shimmering. Add the sliced leeks and cook gently, stirring occasionally, for about 8-10 minutes until they are soft and fragrant with a slight golden hue.
Add the minced garlic and grated ginger to the leeks, stirring continuously for about 1 minute until the mixture is fragrant and the garlic is just beginning to brown.
Sprinkle in the curry powder, cumin, and turmeric, stirring constantly for 1-2 minutes until the spices bloom and release their warm aroma, and the oil takes on a slightly darker hue.
Add the diced potatoes to the pan, stirring to coat them evenly with the spice mixture. Pour in the coconut milk and stir well, scraping up any flavorful bits stuck to the bottom.
Bring the mixture to a gentle simmer, then reduce the heat to low. Cover the pan and cook for 20-25 minutes, stirring occasionally, until the potatoes are tender and the sauce has thickened slightly.
Uncover the pan and check the sauce; if it’s too thick, stir in a splash of water or broth. If it’s too thin, simmer uncovered for a few more minutes until it reaches a velvety consistency.
Turn off the heat and stir in the lemon juice, tasting and adjusting salt and pepper as needed. Let the curry sit for 5 minutes to allow flavors to meld.
Serve the leek and potato curry hot, garnished with fresh herbs if desired, alongside rice or warm naan for a complete, cozy meal.
