Trim the dark green tops from the leeks, then slice the white and light green sections into half-moons about 1 cm thick. Rinse thoroughly in cold water to remove any dirt, then drain and set aside.
Peel the potatoes and cut them into roughly 2 cm cubes. Keep them in water if you're not cooking immediately to prevent browning.
Heat the oil in a large skillet or Dutch oven over medium heat until it shimmers. Add the sliced leeks and cook gently for about 8-10 minutes, stirring occasionally, until they become soft, translucent, and release a sweet aroma.
Add the minced garlic and grated ginger to the leeks. Cook for 1-2 minutes until fragrant, with a gentle sizzle and a warm aroma filling the kitchen.
Sprinkle in the curry powder, turmeric, and cumin. Toast the spices for about 30 seconds, stirring constantly, until they release their warm, earthy scent and turn a slightly darker shade.
Add the diced potatoes to the skillet, stirring well to coat them in the fragrant spices and leeks. Pour in the coconut milk and bring to a gentle simmer.
Reduce the heat to low, cover loosely, and let the curry simmer gently for 20-25 minutes, stirring occasionally. The potatoes should become tender and the sauce will thicken into a velvety, fragrant gravy.
Uncover the skillet, season with salt and pepper to taste. If the curry is too thick, add a splash of water or broth to loosen it, then stir well.
Allow the curry to rest off the heat for about 5 minutes, letting the flavors meld and the sauce to thicken slightly. Taste again and adjust seasoning if needed.
Serve the hot leek and potato curry with rice or crusty bread, garnished with fresh herbs if desired. Enjoy the comforting aroma and creamy texture of this simple dish.