Heat the olive oil in a large heavy-bottomed pot over medium heat until it shimmers and begins to gently bubble.
Add the sliced leeks and cook, stirring occasionally, until they soften and turn translucent, about 8-10 minutes. The aroma should become sweet and oniony, with a gentle sizzle.
Stir in the diced potatoes, coating them with the leek mixture. Cook for another 2 minutes, allowing the flavors to mingle.
Pour in the vegetable stock, ensuring it covers the vegetables. Bring the mixture to a gentle simmer and cook until the potatoes are completely tender, about 15 minutes. You should see the soup bubbling softly with steam rising.
Remove the pot from heat. Use an immersion blender directly in the pot to blend the soup until silky smooth, or carefully transfer in batches to a blender and puree until velvety.
Stir in the heavy cream if using, and season with salt and pepper to taste. Add a squeeze of lemon juice for brightness, blending briefly to incorporate.
Let the soup rest for 5 minutes to allow flavors to meld, then give it a quick stir. Serve hot, garnished with fresh herbs or a drizzle of olive oil if desired.
