Clean the Leeks: Leeks can trap dirt between their layers. Slice off the roots and dark green tops. Cut lengthwise, then soak in cold water for 5 minutes. Rinse well and slice thinly.
Prep the Potatoes: Peel Yukon Gold potatoes and cut into evenly sized 1-inch chunks for consistent cooking.
Saute the Leeks: In a large Dutch oven or heavy-bottomed pot, melt butter over medium heat. Add leeks and a pinch of salt. Sauté 8–10 minutes until soft and translucent. Avoid browning. Add garlic and cook for 1 minute until fragrant.
Simmer: Add potatoes, chicken broth, and thyme. Bring to a boil, then reduce heat to medium-low. Simmer partially covered for 20–25 minutes until potatoes are fork-tender.
Blend until Smooth: Use an immersion blender directly in the pot, or carefully blend in batches in a countertop blender until silky smooth.
Finish with Cream: Stir in heavy cream and simmer gently for 5 minutes. Season with salt and pepper to taste.
Garnish and Serve: Top with fresh chives and a drizzle of olive oil if desired. Serve warm with crusty bread or a side salad.