Heat a large heavy-bottomed pot over medium heat and add a tablespoon of olive oil. Once shimmering, add the diced onion and cook for 5-7 minutes, stirring frequently, until translucent and slightly golden, filling the kitchen with a sweet, caramelized aroma.
Add the minced garlic to the pot and cook for about 30 seconds, stirring constantly, until fragrant and slightly golden. Be careful not to burn the garlic, as this can turn bitter and overpower the soup's delicate flavor.
Pour in the vegetable broth and bring it to a gentle simmer. Carefully add the fresh spinach in batches, stirring until each batch wilts down, about 2-3 minutes per batch. Continue until all the greens are tender and bright green, filling the air with fresh, leafy aroma.
Sprinkle in the smoked paprika, then season with salt and freshly ground pepper. Stir well to distribute the smoky spice evenly, and let the mixture simmer for another 5 minutes to deepen the flavors.
Remove the pot from heat. Using an immersion blender, carefully blend the soup directly in the pot until smooth and velvety. Alternatively, transfer the soup in batches to a blender, blending until completely smooth, then returning it to the pot.
Stir in the heavy cream or coconut milk, blending briefly to incorporate, and warm the soup over low heat for another 2-3 minutes. The soup should be rich, smooth, and steaming hot, with a vibrant green hue and silky texture.
Taste the soup, then adjust seasoning with additional salt, pepper, or smoked paprika as desired. If the soup is too thick, add a splash of warm broth or water to reach your preferred consistency, blending again if needed.
Serve the hot, velvety soup in bowls, garnished with a drizzle of cream or a sprinkle of fresh herbs if desired. Enjoy immediately for the best flavor and texture, savoring the smoky richness in every spoonful.