Step 1

Cut the leeks in half lengthwise. Fill a large bowl with water, submerge the leek halves and swish them around to remove the grit between the layers. Pour off the water and repeat until the leeks are clean, then pat dry. Cut the leeks on the diagonal into 2-inch sections, keeping the layers intact as much as possible.

Step 2

In a 12-inch skillet, combine the oil and the leeks. Set the pan over medium-high and cook, gently stirring only once or twice so the layers do not separate, until the leeks are lightly browned, 4 to 6 minutes. Add ¼ teaspoon salt and ½ teaspoon pepper, then slowly add ⅔ cup water. Add the thyme sprigs, cover and reduce to medium-low. Cook, occasionally shaking the skillet, until a knife inserted into the leeks meets no resistance and most of the water has evaporated, about 20 minutes.

Step 3

Using a slotted spoon, transfer the leeks to a platter, leaving the oil in the skillet. Remove and discard the thyme sprigs. Add the vinegar and honey to the pan, then cook over medium, stirring often, until the mixture is syrupy, 2 to 4 minutes. Taste and season with salt and pepper, then pour over the leeks. Sprinkle with the chopped thyme and the almonds.