Add oil to a non-reactive skillet over medium high heat. Heat until shimmering, add garlic and onion and cook until translucent. Add the barley and cook while stirring for 5 minutes. Add the wine and 6 cups of stock. Bring to a boil, then lower to a simmer. Cover the pan and cook for 25 minutes, stirring occasionally. Add the broccoli and the rest of the stock, if needed. Stir together and cover. Leave on simmer for 10 more minutes. Take off the heat, remove cover and add salt and pepper to taste.