Heat olive oil in a large pot over medium heat until shimmering. Add the minced garlic and cook, stirring frequently, until fragrant and just beginning to turn golden, about 1 minute.
Add the chopped tomatoes and smoked paprika to the pot. Stir well, and cook until the tomatoes start to release their juices and soften, about 8-10 minutes. The mixture should smell fragrant and look slightly saucy.
Pour in the apple cider and stir, scraping any flavorful bits from the bottom of the pot. Bring the mixture to a gentle simmer and cook uncovered for about 10 minutes, allowing the flavors to meld and the soup to slightly reduce.
Using an immersion blender or carefully transferring the mixture to a blender, puree the soup until smooth and velvety. Return to the pot if using a regular blender, and warm over low heat.
Season the soup with salt and pepper to taste. Give it a good stir, then ladle into bowls. Finish each serving with torn basil leaves for a burst of fresh, peppery aroma.
Savor the soup hot, noticing its silky texture and balanced sweetness and acidity, complemented by the inviting aroma of roasted garlic and basil.
