Preheat your oven to 400°F (200°C). Toss the eggplant cubes with 1 tablespoon olive oil, salt, and pepper on a baking sheet. Add the whole garlic cloves.
Roast for 25-30 minutes, stirring halfway through, until the eggplant is golden brown and tender.
In a large pot, heat the remaining olive oil over medium heat. Add the chopped onion and cook until translucent, about 5 minutes.
Add the roasted eggplant, garlic, cumin, and smoked paprika. Stir to combine and cook for 2 minutes to toast the spices.
Pour in the vegetable broth and bring to a simmer. Cook for 10 minutes to let the flavors meld.
Add the spinach and cook until just wilted, about 2 minutes.
Using an immersion blender (or transfer to a regular blender), blend until smooth and creamy.
Taste and adjust seasoning with salt and pepper.