Heat the oil in a large skillet over medium-high heat. Add the onions, 1/2 teaspoon salt and 1/8 teaspoon pepper, and cook, stirring occasionally, until lightly browned, about 5 minutes. Stir in the barley and thyme, and cook, stirring, until the barley is just golden, about 2 minutes more.
Transfer the barley mixture to a 6-quart slow cooker, and add the broth, 1 1/2 cups water and 1/2 teaspoon salt. Cover, and cook on high until the liquid is absorbed and the barley is tender, about 3 hours.
Discard the thyme, and stir in the asparagus. Return the lid to the pot, and cook until the asparagus is tender, 30 minutes more. Stir in the Parmesan, lemon zest, 1 teaspoon salt and 1/4 teaspoon pepper. Thin out the risotto to the desired consistency with warm water, as needed. Fold in the parsley and mint, and serve with lemon wedges on the side.
If your asparagus seem extra woody, give the stalks a quick peel before cutting.
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