Toast the pecans: heat a small skillet over medium heat. Cook the pecans for a few minutes until slightly brown and fragrant. Transfer to a bowl to cool.
Toast the barley: In a 10 inch skillet, add 1 tablespoon of the olive oil. Over medium heat, add the barley to the skillet. Toast 5 minutes. Add 3 cups of water to the skillet, bring to a boil then simmer for 25-30 minutes until the barley is tender.
Heat the remainder of the oil in another 10 inch skillet over medium heat. Sauté the onion for 3 minutes. Mix in the garlic, broccoli and lemon juice. Cook 8-10 minutes until the broccoli is bright green. Transfer this mixture to a large serving bowl.
Add the cooked broccoli to the bowl with the broccoli mixture. Mix in the vinegar, cliantro and pecans. Serve warm or chilled.