Pea shoots are the young, tender tips and vines of the snow pea or the sugar snap pea plant. Once your plants are established and producing an abundance of pods, clip off leaf and tendril sections about 4 inches long. If you don’t have your own plants, look for these tender shoots at farmers’ markets or Asian grocery stores.
Sambal oelek (or ulek) is an Indonesian chile paste, and tart, citrusy Kaffir lime leaves are used in Southeast Asian cooking. Look for both products in Asian markets.
Bring a large saucepan 1/2 full of salted water to a boil over high heat. Add the snap peas and English peas and cook until tender-crisp, about 1 minute. Using a slotted spoon, transfer the vegetables to a colander and rinse under cold water. Set aside.
Return the saucepan to a boil, add the barley, and cook until tender, about 45 minutes. Drain and set aside.
In a small bowl, whisk together the rice vinegar, soy sauce, water, brown sugar, and sambal oelek until blended.
In a large, heavy frying pan over high heat, warm the sesame oil. Add the green garlic, scallions, and lime leaves and stir-fry until the scallions are tender, about 30 seconds. Add the reserved snap peas, peas, and barley along with the pea shoots, and stir to coat.
Pour in the soy sauce mixture and stir and toss until the peas and pea shoots are tender and the liquid is absorbed, about 4 minutes. Transfer to a warmed serving dish and serve.