1. In a pan, warm oil over medium heat. Add shallot and garlic; cook, stirring occasionally, until tender, about 5 minutes. Season with 1/4 tsp. each salt and pepper. Add wine; cook until liquid has almost evaporated, 2 to 3 minutes. Stir in barley and thyme; cook, stirring, for 1 minute. Add 4 cups water and bring to a boil.
2. Cover, reduce heat to medium-low and simmer until barley is tender but still chewy, about 35 minutes. Remove and discard thyme sprigs. Add 1/4 tsp. salt, cheese and peas and stir until cheese is incorporated. Stir in arugula, herbs and lemon juice. Divide among 4 bowls and drizzle with additional olive oil, if desired. Serve immediately.