2 tablespoons extra-virgin olive oil, plus more for brushing
1 onion, finely diced
2 carrots, thinly sliced
4 ounces shiitake mushrooms, stemmed and thinly sliced
1/4 cup dry white wine
1 1/2 cups cooked pearl barley
2 cups cooked white beans, drained and rinsed
2 tablespoons all-purpose flour
4 cups vegetable stock, preferably homemade
2 tablespoons chopped fresh flat-leaf parsley, plus more for garnish
6 sheets frozen phyllo dough, preferably whole wheat, thawed
Sea salt, for sprinkling
Heat olive oil in a large skillet over medium. Sauté onion, carrots, and mushrooms until tender, stirring frequently, 6 to 8 minutes. Add wine; cook, stirring up browned bits, until almost all the wine has evaporated.
Combine barley and beans in a large pot. Whisk flour into stock and add to pot. Bring to a boil and cook, stirring, until slightly thickened. Remove from heat. Stir in parsley and let cool slightly.
Preheat oven to 425F. Using a 12-ounce ramekin as a guide, cut out 4 rounds from phyllo; keep covered with a damp paper towel.
Spoon barley mixture into 4 ramekins. Brush each cut sheet with oil and place on top of filled ramekin. Cut vents into tops. Sprinkle with sea salt and reserved parsley.
Transfer to a rimmed baking sheet and bake until tops are golden and filling is bubbling, about 30 minutes. Let cool slightly before serving.