Thoroughly clean the leeks, slice them lengthwise, and rinse under water. Chop the Yukon gold potatoes into uniform cubes and grate the garlic.

(Optional) Create a broth by simmering rinsed leek tops in water with thyme, minced garlic, salt, and pepper for about 30 minutes. Strain and set aside.

Melt the unsalted butter in a large pot over medium heat. Add the sliced leeks and a pinch of salt; sauté for 8-10 minutes until softened.

Add the chopped Yukon gold potatoes, grated garlic, and prepared broth or vegetable broth. Stir in fresh thyme. Simmer uncovered for about 20 minutes until the potatoes are tender.

Remove from heat and blend the soup until smooth using an immersion blender.

Return the blended soup to low heat, stir in milk or heavy cream, and adjust seasoning with lemon juice, salt, and pepper. Garnish with chopped chives and serve.