This is an awesome salad to take on a picnic or to a barbecue. Sometimes with grain salads, I feel like grain is too much of the focus—but here, we have equal amounts of asparagus and mushrooms, and all of the ingredients play together beautifully.
For the barley: In a medium stockpot, combine barley, stock, and 1½ teaspoons salt. Bring to a boil, reduce to a simmer, and cook uncovered until barley is cooked through, about 45 minutes.
For the onion mixture: Chop the shallots by cutting off the bottoms to make them flat. Then cut into the shallot lengthwise, leaving the root end intact; cut down and across for a clean dice. Peel the garlic by smashing it with the back of the knife. Remove the peel, cut the hard root off, and thinly slice. Slice the onion at an angle into half-moon shapes. Add 2 tablespoons of olive oil to a skillet over medium heat, followed by the shallots and onion. Add ½ teaspoon salt and the pepper; sweat until translucent, 1–2 minutes. Add the garlic and chili flakes and cook until onions are thoroughly softened. Remove from the skillet and set aside.
For the mushrooms and asparagus: Add 2 tablespoons of olive oil to a skillet over medium-high heat, followed by the mushrooms. Add a ½ teaspoon of salt and cook until they have released their liquid and begun to caramelize around the edges. Add the onion mixture back into the pan and set aside. Meanwhile, trim the asparagus by snapping the tough woody ends where they naturally break. Cut diagonally, on a bias.
Once the grains have opened up and are plump, drain the barley. Spread in a single layer on a sheet tray to cool down. Reheat the mushroom/onion mixture and add the thyme, asparagus, and 2 tablespoons of olive oil. Toss and cook for 1 minute; then remove to the sheet tray with the barley. Use a vegetable peeler to shave the Parmesan; set aside.
Assemble the dish: Place the cooled barley and asparagus mixture into a large mixing bowl. Toss, taste to adjust seasoning, and drizzle the vinegar and 1 teaspoon of olive oil around the edge of the bowl, followed by the Parmesan shavings. Gently toss again, taste for seasoning, and serve.