In a small saucepan, bring broth to a simmer; keep hot.

Add butter and remaining 1 tablespoon olive oil and heat until the butter melts. Add the sliced fennel and chopped onion and cook stirring often, until the vegetables soften, 3 to 5 minutes. Add the barley and stir to coat with the butter and olive oil. Cook for 2 minutes, stirring often, then add the dried thyme, bay leaf, remaining garlic clove, remaining 1/2 teaspoon salt, and remaining 1/4 teaspoon pepper. Cook 1 additional minute. Add the wine. Stir and cook for 2 minutes.

Add 2 full ladles of the stock to the barley. Stir and simmer over medium heat until the stock is absorbed, 5 to 10 minutes. Constant stirring isn’t necessary, but do watch the pot and stir often. Continue adding the stock, 2 ladlefuls at a time, until it is all absorbed and the barley is creamy, but maintains a bit of chew, 25 to 30 minutes total.

(Add hot broth, 1/2 cup at a time, stirring constantly and allowing the liquid to absorb between additions. Cook just until barley is almost tender (cooking time is about 45 minutes). Add the parsley and lemon zest; cook and stir until heated through. Serve immediately.)