Preheat the oven to 425°F.
In a medium pot, combine the barley and 3 cups water. Bring to a boil, then decrease the heat to low and keep it at the laziest simmer. Cover and cook, checking for doneness after 30 minutes. You want the grains to be tripled in size and tender but not mushy. If there is still water left in the pot when they've reached this point—keeping in mind you might have to let them cook another 5 to 10 minutes—you can strain the barley in a colander, the way you strain pasta.
Meanwhile, in a large bowl, toss together the Brussels sprouts, broccoli, olive oil, and some salt and pepper. Spread them out in an even layer on a sheet pan and roast for 20 to 25 minutes, until everything is crispy and browned.
Make the dressing: In a small food processor, whirl together the avocado, olive oil, vinegar, honey, lemon juice, 2 tablespoons water, and some salt and pepper. The final consistency should be thin enough to drizzle, so add more water as necessary. Adjust seasoning to taste.
Divide the barley evenly among four bowls and top with the roasted vegetables, crispy chickpeas, and pickled onions. Drizzle with avocado dressing and serve.