Set a rack in the upper middle of the oven and heat the oven to 425°F.

Put the farro, 5 cups water, and 1/2 teaspoon of the salt into a medium saucepan. Bring it to a boil over high heat.

Put the carrots and red onion on a large sheet pan. Drizzle with 2 tablespoons of the olive oil and sprinkle with 1 teaspoon of the cumin and 1/2 teaspoon of the salt.

Toss the vegetables on the sheet pan until they are evenly coated. Spread them into a single layer so they roast instead of steam.

Slide the sheet pan into the oven. Roast the vegetables for 15 minutes.

When the farro comes to a boil, lower the heat to keep the water at a steady simmer. Cook for 20 to 25 minutes, until the grains are tender but still a little chewy.

Put the drained butter beans into a medium bowl. Add 1 tablespoon of the olive oil, the remaining 1/2 teaspoon cumin, and 1/4 teaspoon of the salt.

Toss the beans gently in the bowl so they stay mostly whole. Make sure they are coated well so they can crisp in the oven.

Take the sheet pan out of the oven. Stir the carrots and onion, then move them toward the outer edges of the pan.

Add the seasoned butter beans to the center of the sheet pan in a single layer. Return the pan to the oven.

Roast for 12 to 15 minutes more, until the carrots are browned at the edges, the onion is soft, and some of the beans look lightly crisp and split open.

Put the Greek yogurt into a small bowl. Add the lemon zest, 1 tablespoon of lemon juice, the remaining 1 tablespoon olive oil, and the remaining 1/4 teaspoon salt.