Put the barley in a medium pot with water to cover by a few inches and salt it generously. Tie the thyme sprigs, parsley stems, and bay leaf together with a piece of kitchen twine and add to the pot, along with the lemon peel. Simmer, stirring occasionally, until tender, about 30 minutes. Drain and remove the herbs and lemon.

Meanwhile, toss the mushrooms with 2 tablespoons of the lemon juice and 1/2 teaspoon of the salt in a large bowl. Whisk the remaining lemon juice with the mustard, remaining salt, and pepper, to taste, in a small bowl. Gradually whisk in the olive oil, starting with a few drops and then adding the rest in a steady stream to make a smooth, slightly thick vinaigrette. Add the shallots.

Toss the mushrooms, barley, and the dressing together. Stir in the chopped herbs. Set aside at room temperature for about 1 hour for the flavors to come together.

Preheat the oven to 450 degrees F.

Spread the spears in a single layer in a shallow baking pan, drizzle with olive oil, sprinkle with salt, and roll to coat thoroughly. Roast the asparagus until lightly browned and tender, about 10 minutes, giving the pan a good shake about halfway through. Spread the roasted asparagus on a serving platter. Spoon the barley salad on top and serve.

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