1/4 cup plus 2 Tbsp. extra-virgin olive oil; more for drizzling
2 tablespoons white wine vinegar
2 tablespoons (packed) light brown sugar
1/2 teaspoon finely grated orange zest
Kosher salt, freshly ground pepper
1 bunch Tuscan kale, center ribs and stems removed, leaves cut into 1-inch squares
1/4 cup minced shallots
3 medium golden beets (about 1 bunch), trimmed
1 1/4 cups pearl barley
4 ounces feta, crumbled
2 teaspoons (or more) unseasoned rice vinegar