Preheat oven to 400ºF. Toss squash in 2 Tbsp. olive oil and kosher salt; spread evenly on a rimmed baking sheet. Place in the oven and bake for 25 to 35 minutes, tossing once halfway through, until the squash is tender and lightly browned.
Meanwhile, combine quinoa and broth in a small saucepan. Bring mixture to a boil, cover, reduce heat, and gently simmer until liquid is absorbed and quinoa is fluffy, about 15 minutes. Transfer to a large bowl.
Prepare Creamy Ginger Dressing by combining all ingredients except oil in a small bowl; stir to combine. Gently stream in oil, whisking constantly, until dressing is smooth.
Add kale to bowl with quinoa, and toss to combine (the residual heat of the quinoa will help soften the kale leaves). Add cabbage, carrots, bell pepper, and butternut squash. Season ingredients with a pinch of salt. Add dressing and gently toss to combine. Stir in peanuts and fresh basil, and garnish with avocado (if using).