Arrange butternut squash into a single layer onto a baking pan. Drizzle 1 tablespoon olive oil on top. Wrap each ear of corn in aluminum foil.
Bake in the preheated oven until squash is tender, about 15 minutes. Continue cooking corn until charred, about 15 minutes more.
Cut corn kernels off cob; place in a container with the butternut squash.
Heat 1 tablespoon olive oil in a skillet over medium heat. Add red onion; cook and stir until softened and translucent, about 5 minutes. Add cranberries; cook and stir until soft and slightly plump, 5 to 7 minutes. Transfer onion and cranberries to the squash mixture.
Combine the remaining 2 tablespoons olive oil, lemon juice, chile paste, garlic powder, vinegar, and paprika in a bowl. Toss with the cranberry-squash mixture. Mix cilantro into the salad.