How to Make It
Make the lentils In a large saucepan, cover the lentils with 2 inches of water and bring to a boil. Simmer over moderate heat until just tender, 20 minutes. Remove from the heat, add a generous pinch of salt and let stand for 5 minutes; drain. Spread the lentils on a rimmed baking sheet and let cool slightly.
Meanwhile, preheat the oven to 400°. On a large rimmed baking sheet, toss the carrots and parsnips with the cumin, coriander, chile powder and 1/4 cup of the olive oil. Season generously with salt and pepper. Roast the vegetables until tender and browned in spots, 20 to 25 minutes.
In a large bowl, toss the lentils with the warm roasted vegetables, the lemon juice and the remaining 1/4 cup plus 2 tablespoons of olive oil. Fold in the chopped mint and cilantro and season the salad with salt and pepper. Transfer to a platter and garnish with mint and cilantro leaves.
Make the tzatziki In a small bowl, whisk all of the ingredients together and season with salt and pepper. Serve alongside the warm lentil salad.
Coconut milk yogurt is dairy-free and can be found in the refrigerated section of most grocery stores.