How to Make It
Trim root end of each leek, leaving enough root to keep leaves attached. Halve leeks lengthwise. Submerge leeks in a bowl of water; clean grit from between leaves.
Heat a large, high-sided saucepan over medium. Add oil; swirl to coat. Add leeks, cut side down, and cook 6 minutes or until browned on both sides, turning once. Why? Browning the leeks adds caramelized flavor to the braising liquid. If needed, work in 2 batches to prevent overcrowding the pan.
Arrange leeks, cut side up, in pan; sprinkle with salt. Add wine, stock, and thyme; cover and reduce heat to medium-low. Gently simmer 15 to 18 minutes or until leeks are very tender. Remove leeks to a platter, leaving braising liquid in pan. Why? The acidic wine brightens what will later become a light sauce. Covering the pan keeps the liquid from completely evaporating.
If needed, cook liquid 30 to 60 seconds or until liquid is reduced to about 3 tablespoons. Add butter to pan; swirl to melt. Discard thyme sprigs. Pour liquid over leeks, and sprinkle leeks with parsley. Why? Reducing concentrates the liquid. The butter adds flavor and body to the sauce.