Rinse the leeks well, remove any outer layers if they are damaged, and slice them into 1/2 inch rounds. You should have roughly 2/3 pound of leek rounds. As you are slicing the leeks, you may notice some sand in between the layers, particularly closer to the light green parts. If you see any bits of soil or sand, try to rinse it away while keeping the leek rounds intact.
Place the leek rounds in one layer at the bottom of a sautee pan that has a lid. Make sure they are flat against the bottom of the pan. Add the 2/3 cup sherry/wine, 2 cloves crushed garlic, and 4 sprigs thyme to the pan. Add enough water to barely cover the leeks without letting them float around too much.
Place the pan over medium-high heat and bring to a simmer. Once the liquid comes to a simmer, add a pinch of salt to the cooking liquid and allow it to dissolve. Taste the cooking liquid and adjust the seasoning of the cooking liquid until it is pleasantly seasoned, not salty. Cover with a lid, turn the heat down to maintain a gentle simmer, and cook for 15-20 minutes
After 15-20 minutes, taste one of the leek rounds, it should be very tender, if not, keep cooking. When the leeks are tender, carefully remove them from the poaching liquid using a spatula. Put them on a plate and place in the refrigerator until completely cool.