Preheat the oven to 400 degrees and prepare a sheet pan with cooking spray or parchment paper.
Combine the spices, brown sugar, and sea salt in a small bowl and stir to combine thoroughly.
Peel and cut the carrots in half lengthwise, then cut into 2-inch long pieces. If there are any particularly fat parts of the carrots, cut those into quarters. Add the carrots to the sheet pan.
Drizzle the carrots with the extra virgin olive oil and toss them to coat, then sprinkle with the seasoning and toss again. Make sure the carrots are spread out in a single layer and roast for 20 minutes.
Working quickly, take the pan out of the oven and close the oven. Use a spatula to turn over the carrots (try to get every one turned over), then return the pan to the oven and roast for another 15-20 minutes.
Prepare the toppings while the carrots are roasting. Combine the yogurt and apple juice in a small bowl and set aside, and chop the parsley and the walnuts.
Check the carrots for doneness, a fork should easily pierce the largest pieces. When done, remove to a serving bowl or platter and drizzle with the yogurt mixture. Sprinkle on the walnuts and parsley and serve.
Notes
Chili powders vary dramatically between types, brands, and even batches. I buy a mild chili powder in the Mexican food aisle that has no heat, and will blend it in with whatever chili powder I’m using to cut the heat without sacrificing flavor. Ancho chili powder is also quite mild and would work great for these spice roasted carrots, or you can substitute equal parts paprika and cumin. Apple verjus is the pressed juice of tart apples that are harvested in early summer before they ripen. It has a pleasing acidity just below that of lemon juice. It is available online. Apple juice and apple cider also work in this recipe, especially unsweetened versions if you can find them.