Saute chorizo in a large stockpot over medium high heat until cooked, about 3-5 minutes, stirring occasionally. Remove chorizo with a slotted spoon. Reserve 2 tablespoons of grease in the stockpot, and discard the rest.
Add onion to the stockpot, and saute in the chorizo grease for 5 minutes or until soft and translucent, stirring occasionally. Add garlic and brussels sprouts, and saute for an additional 3 minutes or until the brussels sprouts begin to brown, stirring occasionally. Add chicken broth, potatoes, paprika, salt and pepper, and stir to combine. Bring to a boil, then reduce heat to medium-low, cover and simmer for 10-15 minutes, or until the potatoes are tender.
If you would like a pureed soup, blend soup using an immersion blender or stand blender. If you would like a chunkier soup, leave it as is. Stir in evaporated milk and chorizo, reserving 1/4 cup chorizo for toppings if desired. Season with additional salt and pepper if needed.