Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper.
Combine the carrots, potatoes and Brussels sprouts in a large bowl. Drizzle with 1/4 cup olive oil and sprinkle with the salt, pepper and coriander. Spread the vegetables on the prepared baking sheet and roast for 15 to 20 minutes. Flip the vegetables and continue to roast until tender and browned all over, 15 to 20 minutes more.
Meanwhile, add the feta, yogurt, honey, lemon zest and lemon juice to a food processor and pulse until smooth and creamy, adding a little water if needed to loosen the puree. Add the herbs and pulse until just distributed (you don't want to turn the mixture green; you just want to combine them). Spread the feta mixture on a platter. Arrange the roasted vegetables on top of the feta. Sprinkle the pomegranate seeds and pistachios over the top and finish with a drizzle of olive oil.