Heat the oven to 425 degrees. On a parchment-lined sheet pan, toss together the mushrooms, scallions, halloumi and 3 tablespoons oil; season with salt and pepper. (The pan might be crowded, but that’s OK.) Roast on the bottom rack until crisp and golden, 25 to 30 minutes.
Meanwhile, in a large saucepan, cover the barley with 2 inches of water and season with salt. Bring to a boil over high heat. Reduce heat and simmer until tender, 15 to 20 minutes. Drain, rinse under cold water, then leave in the strainer to drain again. Hold onto the saucepan; there is no need to wash it at this stage.
In a small bowl, stir together the yogurt and olives; season to taste with salt and pepper.
When the mushroom mixture is done roasting, finely grate the zest of the lemon over it and stir to combine. Shake the barley to get rid of any water, then transfer it back to the saucepan, along with the raw vegetables, herbs and the remaining 1 tablespoon oil. Halve the lemon and squeeze enough juice into the barley mixture until it tastes peppy and fresh (about 2 tablespoons); season to taste with salt and pepper.
Spoon and spread out a small amount of the barley into bowls, then add small spoonfuls of yogurt and top with a layer of the mushroom mixture. Repeat with another layer of barley, yogurt and mushrooms. Drizzle with olive oil. Leftovers will keep for up to 2 days refrigerated. Adjust seasonings with salt and lemon juice.