**Get the broth ready.** If using stock cubes, dissolve them in 6 cups (1.4L) of hot water and stir until clear and golden. Using a carton? Measure 6 cups and set aside.
**Wash and prep the leeks.** Cut off the dark green tops and root ends. Thinly slice the white and pale green parts into rounds. Transfer to a bowl of cold water, swish well, then lift out with your hands (leaving the grit behind). Mince the garlic. Peel and dice the potatoes into 1-inch (2.5cm) cubes.
**Soften the leeks.** Melt the butter in a large pot over medium-low heat. Add the leeks and a pinch of salt. Cook, stirring often, for 8–10 minutes until very soft and translucent — no browning. Reduce heat if the edges start to color.
**Add garlic.** Stir in the minced garlic and cook 1 minute until fragrant.
**Simmer.** Add the diced potatoes, broth, and thyme. Bring to a gentle boil, then lower to a steady simmer. Cook for 20–25 minutes, until the potatoes are very tender — a fork should slide in easily with no resistance.
**Blend just until smooth.** Remove and discard the thyme sprigs. Use a stick blender directly in the pot, or carefully ladle batches into a countertop blender (fill no more than halfway; hold the lid down firmly with a folded kitchen towel). Blend until just smooth, then stop immediately. Over-blending makes the soup gluey.
**Finish.** Set heat to low. Stir in the cream and lemon juice. Taste and season generously with salt and black pepper.
**Serve.** Ladle into bowls. Top with chopped chives, a drizzle of olive oil, and cracked black pepper. Serve with crusty bread.
