Leeks Simmered in Olive Oil

Ingredients

• 2 pounds leeks, roots trimmed, thick outer skins removed
• 1/3 cup chopped onion
• 1/4 cup extra-virgin olive oil
• 2 medium carrots, peeled and sliced
• 2 teaspoons sugar
• 1 tablespoon rice, preferably medium-grain
• Salt and freshly ground pepper
• Juice of 1/2 lemon, or more to taste
• 1/4 cup chopped flat-leaf parsley