Meanwhile, in a large deep skillet, bring 1/2 inch of water to a boil. Add the broccoli florets, cover and cook just until bright green, about 2 minutes. Drain and pat dry. Wipe out the skillet and melt 1 tablespoon of the butter in the olive oil. Add the broccoli stems and stir-fry over high heat until crisp-tender, about 2 minutes. Add the shallots, ginger and jalapeño and stir-fry for 1 minute. Add the broccoli florets, season with salt and stir-fry for 2 minutes. Off the heat, stir in the barley and scallion and the remaining 1 tablespoon of butter. Transfer to a bowl and serve warm.