Trim the ends and dark green tops from the leeks and discard. Cut the leeks in half lengthwise, then crosswise into 1-inch pieces. Immerse the leeks in a bowl of cold water, swish to remove any grit and lift the leeks out into a colander. Clean the bowl, change the water and repeat until the water remains clear. You should have 6 cups leeks.
Add the leeks, carrots, oil and a generous pinch each of salt and pepper to a high-sided medium skillet over medium heat and bring to a steady sizzle, stirring occasionally. Stir in 2 tablespoons water, bring to a simmer and cover. Reduce the heat to medium-low and simmer until the vegetables are tender, about 20 minutes.
Zest the lemon directly over the vegetables. Squeeze 1 tablespoon lemon juice into the mixture and stir in the dill. Season with salt and pepper. Serve warm or at room temperature with lemon wedges.
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