Preheat the oven to 425°F (220°C).
Place the cubed butternut squash and zucchini pieces on a large baking sheet. Drizzle with 1 tablespoon of olive oil and toss to coat evenly.
Spread the vegetables in a single layer and roast in the preheated oven for 30-35 minutes, turning halfway through, until tender and lightly caramelized.
While the vegetables roast, heat the remaining 1 tablespoon of olive oil in a large pot over medium heat.
Add the chopped onion and sauté for 5-7 minutes until translucent and softened.
Add the minced garlic, ground cumin, smoked paprika, and dried thyme to the pot. Cook for 1-2 minutes, stirring frequently, until fragrant.
Once the roasted vegetables are done, add them to the pot with the onions and garlic.
Pour in the vegetable broth and bring the mixture to a boil. Reduce heat to low and simmer for 10 minutes to allow flavors to meld.
Using an immersion blender, blend the soup until smooth and creamy. Alternatively, carefully transfer the soup in batches to a blender and puree until smooth, then return to the pot.
Season the soup with salt and freshly ground black pepper to taste. Stir well.
Ladle the soup into bowls and garnish each serving with a dollop of Greek yogurt and a sprinkle of chopped fresh parsley.
Serve warm and enjoy.