Begin by slicing the leeks thinly, about 1 cm thick, and rinse them thoroughly under cold water to remove any grit. Set aside.
Peel the potatoes and dice them into uniform 1-2 cm cubes, which helps them cook evenly. Set aside.
Heat the butter or olive oil in a large heavy-bottomed pot over medium heat until shimmering and fragrant. Add the sliced leeks with a pinch of salt and sauté gently, stirring often, until they turn translucent and soft—about 8 minutes. The aroma will sweeten and fill the kitchen.
Add the minced garlic to the leeks and cook for another minute, stirring constantly, until fragrant but not browned. The garlic should release a lovely aroma and become slightly golden.
Stir in the diced potatoes, coating them with the leek mixture. Let them cook together for about 2 minutes, allowing the flavors to mingle and the potatoes to start softening.
Pour in the vegetable broth, bringing the mixture to a gentle boil. Once bubbling, reduce the heat to low, cover the pot, and let it simmer for about 20 minutes, until the potatoes are tender and easily pierced with a fork.
Uncover the pot and use an immersion blender directly in the soup to blend until completely smooth and velvety. If using a regular blender, carefully transfer the soup in batches, blending until silky, then return to the pot.
Taste the soup and adjust the seasoning with salt, pepper, and a pinch of nutmeg or thyme if desired. For added richness, swirl in the cream or dairy-free alternative, stirring well to combine.
Serve the hot soup in bowls, garnished with fresh herbs if you like. Pair with crusty bread for a cozy, satisfying meal.
