Preheat the oven to 400 degrees F. Place the cubed squash on a baking sheet, drizzle with 1 tablespoon olive oil, and sprinkle with the turmeric, salt, and black pepper. Toss to coat evenly, then spread in a single layer.
Roast the squash for 25 to 30 minutes until the edges turn golden and the pieces are tender when pierced with a fork.
While the squash roasts, heat the remaining 1 tablespoon olive oil in a large pot over medium heat. Add the chopped onion and cook for 5 minutes until softened. Stir in the minced garlic and cook for 1 minute more.
Pour in the vegetable broth and add the roasted squash. Bring the mixture to a simmer and cook for 10 minutes to let the flavors combine.
Remove the pot from the heat. Use an immersion blender to puree the soup until smooth, or transfer it in batches to a countertop blender. Taste and adjust salt if needed.