Preheat the oven to 425°F (220°C).
Place the halved tomatoes, cubed eggplant, quartered onion, and whole garlic cloves on a large baking sheet.
Drizzle 2 tablespoons of olive oil over the vegetables and sprinkle with 1/2 teaspoon salt and 1/4 teaspoon black pepper. Toss to coat evenly.
Roast the vegetables in the preheated oven for 30 minutes, turning halfway through, until they are tender and slightly caramelized.
Remove the vegetables from the oven and let them cool slightly.
In a large pot, heat the remaining 1 tablespoon of olive oil over medium heat.
Add the roasted vegetables to the pot along with the vegetable broth, dried thyme, smoked paprika, tomato paste, remaining 1/2 teaspoon salt, and 1/4 teaspoon black pepper.
Bring the mixture to a simmer and cook for 10 minutes to allow the flavors to meld.
Using an immersion blender, carefully blend the soup until smooth. Alternatively, transfer the soup in batches to a blender and puree until smooth, then return to the pot.
Stir in the fresh lemon juice and adjust seasoning with additional salt and pepper if needed.
Serve hot, garnished with a drizzle of olive oil or fresh herbs if desired.