Rinse the quinoa under cold water in a fine-mesh strainer. In a medium saucepan, combine the rinsed quinoa with 2 cups of water and a pinch of salt. Bring to a boil, then reduce the heat to low, cover, and simmer for about 15 minutes or until the quinoa is cooked and the water is absorbed. Fluff with a fork and set aside to cool.
While the quinoa is cooling, finely slice the purple cabbage, red bell pepper, and green onions. Grate or julienne the carrots. Place all the prepared vegetables in a large mixing bowl.
In a medium bowl, combine the peanut butter, low sodium soy sauce, rice vinegar, sesame oil, brown sugar, lime juice, minced garlic, grated ginger, and chili garlic sauce. Whisk until smooth and well combined. Taste and adjust the seasoning, adding more chili garlic sauce if you prefer extra heat.
Once the quinoa has cooled, add it to the bowl with the vegetables. Pour the spicy peanut sauce over the salad and toss everything together until the quinoa and veggies are well coated in the sauce. If using, fold in the fresh basil for an aromatic touch.
You can serve the Spicy Peanut Quinoa Salad immediately, or let it chill in the refrigerator for about 30 minutes to allow the flavors to meld.