Preheat the oven to 425°F.
Roast the garlic: Cut the top ½ inch off of the garlic head. Tear a piece of foil (enough to wrap around the garlic) and place the garlic head in the middle. Drizzle olive oil on top, letting it seep into the garlic cavities. Wrap the garlic up and place it in the oven. Roast the garlic until squidgy and golden inside, about 45 minutes. Set aside to cool.
Make the roasted garlic chive yogurt sauce. In an upright blender or mini food processor, combine all of the roasted garlic minus 1 clove, the non-dairy yogurt, lemon juice, tahini, chives, onion powder, salt, and pepper. Mix until totally smooth. If you’re using a full size blender, you may need to add a few splashes of water to get the blade going. Once the sauce is done, check it for seasoning, adjust if necessary, and set aside.
Place the lentils in a medium saucepan and cover them by 2 inches of water. Bring them to a boil and then lower the heat to a simmer. Cook until the lentils are just tender, about 20 minutes. While lentils are cooking, in a sealable jar, combine the reserved roasted garlic clove, red wine vinegar, worcestershire sauce, dijon, olive oil, salt, and pepper. Give it a good shake. The roasted garlic clove should be soft enough to “mash” itself up in the dressing.
Once the lentils are cooked, drain and transfer them to a medium bowl. Immediately cover them with the red wine vinegar dressing and add a few good pinches of salt and pepper. Toss to combine and set aside.
Preheat your grill to medium high. If some of your carrots are quite thick, cut them in half lengthwise. Lay the carrots out on a plate or baking sheet. Give them a drizzle of olive oil and a sprinkle of salt and pepper. Toss to coat.
Place the carrots on the grill, in the opposite direction of the grates, and immediately lower the heat to medium. Cook the carrots, turning them regularly. You want char marks on all sides. Keep cooking them until tender all the way through, about 15-20 minutes.
On a platter, spread out the lentils. Arrange the carrots on top. Drizzle the carrots with the roasted garlic chive yogurt sauce. Top with more chopped chives if you like, as well as the sesame seeds. Serve immediately.