1. 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.
2. 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.
3. Preheat oven to 425°F. 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.
4. Transfer to a rimmed baking sheet and bake until tops are golden and filling is bubbling, about 30 minutes. Let cool slightly before serving.