Instructions

1. Make the labneh:
2. Line a fine-mesh strainer with cheesecloth or a clean, lint-free kitchen towel and place over a bowl.
3. Juice 1/2 medium lemon into a small bowl until you have 2 teaspoons. Add 2 cups plain whole-milk yogurt and 1 teaspoon kosher salt and stir to combine. Transfer to the strainer. Refrigerate uncovered at least overnight or up to 2 days. The longer you strain it, the thicker the labneh will be.
4. Make the vegetables:
5. Heat and outdoor grill for medium-high, direct heat. Meanwhile, peel 1 pound carrots and trim the stem ends. Trim the root end and the dark green tops from 4 large leeks so only the white and lightest green parts remain (save the tops for stock), and remove the outer leaves. Halve the leeks lengthwise. Place in a bowl of water. Working with 1 leek at a time, use your hands to ruffle the layers of the leeks in the bowl of water to remove any sediment. Lift the leeks out of the water and dry on a kitchen towel.
6. Place the carrots and leeks on a rimmed baking sheet. Drizzle with 2 tablespoons olive oil, season with 3/4 teaspoon kosher salt and 1/2 teaspoon black pepper, and toss to coat. Cut 1/2 medium lemon into 4 wedges.
7. When the grill is ready, scrub the grill grates clean if needed. Place the carrots and leeks cut-side down on the grill grates. Cover and grill undisturbed until grill marks form on the bottom, 5 to 7 minutes.
8. Flip the carrots and leeks. Place the lemon wedges cut-side down on the grill. Grill uncovered until the carrots and leeks are fork tender, about 5 minutes more for the leeks and lemons and 9 to 10 minutes for the carrots. Meanwhile, pick the leaves from 3 to 4 fresh dill sprigs until you have 1 tablespoon and coarsely chop.
9. Spread the labneh on a serving platter, and arrange the grilled carrots and leeks on top. Squeeze 1 lemon wedge over the top and garnish with the dill. Sprinkle with Aleppo chile flakes if desired and serve with the remaining lemon wedges.