In a medium bowl, soak hulled barley in warm water to cover for 4 hours. Drain.
In a medium saucepan over medium heat, bring barley and 2 cups water to a boil. Cover, reduce heat to low, and cook for 40 minutes or until water is absorbed and barley is tender. Let cool.
Preheat a grill top or grill to medium.
Grill asparagus on all sides for about 5 minutes. Chop asparagus into 2-inch pieces, and place in a large bowl.
Grill red bell pepper on all sides for about 20 minutes or until charred. Immediately place pepper onto a plate, cover with plastic wrap, and set aside to cool for 10 minutes.
Peel skin off red pepper (it's okay if it doesn't all come off), and remove the stem, ribs, and seeds. Slice pepper into [1/4]-inch strips, and add to the large bowl.
Add barley to asparagus and red bell pepper. Add artichoke hearts, cherry tomatoes, parsley, 2 tablespoons extra-virgin olive oil, balsamic vinegar, salt, and black pepper, and toss to combine.
Cut goat cheese into 4 equal pieces, and coat all sides of cheese with panko breadcrumbs.
Preheat a small skillet over low heat, and add remaining 2 tablespoons extra-virgin olive oil. Add panko-coated goat cheese slices, and brown on both sides for about 2 minutes per side.
To serve, place [1/4] of salad mixture on a plate, top with 1 goat cheese slice, and serve immediately.