Preheat your oven to 400°F (200°C).

Prepare the poblano peppers: Place the poblano peppers on a baking sheet. Roast for 20-25 minutes, turning halfway through, until the skins are blistered and lightly charred. Alternatively, you can char them over an open gas flame on your stovetop.

Steam and peel the peppers: Once roasted, immediately transfer the peppers to a bowl and cover tightly with plastic wrap or a lid. Let them steam for about 10-15 minutes. This will make them easier to peel. Once cool enough to handle, peel off the charred skin, remove the stems and seeds, and roughly chop the pepper flesh.

Sauté aromatics: While the peppers are steaming, heat 1 tablespoon of olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion and cook until softened and translucent, about 5-7 minutes. Add the minced garlic and cook for another minute until fragrant.

Simmer the soup: Add the chopped roasted poblano peppers, vegetable broth, milk (or half-and-half), cumin, and smoked paprika to the pot. Bring the mixture to a simmer, then reduce the heat to low, cover, and let it cook for about 15 minutes to allow the flavors to meld.

Blend until smooth: Remove the pot from the heat. Using an immersion blender, carefully blend the soup until it reaches your desired smoothness. If you don't have an immersion blender, you can transfer the soup in batches to a regular blender (be cautious with hot liquids – vent the lid and cover with a towel).

Season and serve: Return the soup to the pot if necessary. Season generously with salt and freshly ground black pepper to taste. Reheat gently if needed. Ladle the soup into bowls and top with your favorite garnishes.