Preheat the oven to 375°F. Line a 9x13x2 baking dish with parchment paper.
Place the chopped carrots and beets in the baking dish and toss them with the olive oil, za’atar, salt and pepper. Once the vegetables are evenly coated, spread them out into a single layer and slide the dish into the oven. Roast the vegetables for 1 hour, taking them out at the halfway point to stir them up and flip them over.
Make the herbed jalapeño yogurt sauce: In a food processor, combine the herbs, jalapeño, garlic, pistachios, olive oil, lemon juice, salt, and pepper. Pulse the machine a few times until everything is finely chopped, scraping down the sides of the bowl with a spatula if necessary. Add the non-dairy yogurt to the food processor and pulse until the sauce is fully combined and uniformly light green. Check the sauce for seasoning and adjust if necessary.
To serve: Spread the herbed jalapeño yogurt sauce out on the base of your serving plate. Pile the roasted root vegetables on top of the yogurt sauce.
Garnish the grounding roasted roots and herbed jalapeño yogurt sauce with extra chopped herbs and pistachios. Serve warm or at room temperature.