Prep the leeks. Cut off the dark green tops and root ends. Slice the leeks lengthwise, then into half-moons. Rinse thoroughly in a bowl of water to remove grit.
Drain well.
Sweat the aromatics. In a large pot, melt the butter over medium heat. Add the leeks and onion with a pinch of salt. Cook 8–10 minutes, stirring occasionally, until softened and sweet but not browned.
Add the garlic and cook 30 seconds until fragrant.
Add potatoes and liquid. Stir in the diced potatoes, broth, bay leaf, 1 teaspoon salt, and 1/2 teaspoon pepper. Bring to a gentle boil, then reduce to a simmer.
Simmer until tender. Cook 15–20 minutes, or until the potatoes are easily pierced with a fork. Remove and discard the bay leaf.
Blend to desired texture. Use an immersion blender to puree until silky-smooth.
For a rustic soup, blend only part of it and leave some chunks. If using a countertop blender, work in batches and vent the lid slightly to release steam.
Finish with cream. Stir in the cream and warm through on low heat. Don’t boil.
Taste and adjust with more salt and pepper. Add lemon juice if you like a brighter finish.
Serve. Ladle into bowls and garnish with chives, a drizzle of olive oil, or a small knob of butter. Crack on extra black pepper for a little heat.