Start by gathering all the ingredients and prepping them for the chowder. Peel and devein the shrimp, removing the tails. Dice the potatoes, onion, and celery. Mince the garlic and chipotle peppers. Measure out the broth, spices, and heavy cream.
In a large pot or Dutch oven, heat a tablespoon of olive oil over medium heat. Add the diced onion and celery, and sauté for 5-7 minutes, or until the vegetables are softened and fragrant. Stir in the minced garlic and continue cooking for an additional minute.
Add the diced potatoes and the broth to the pot. Bring the mixture to a boil, then reduce the heat to medium-low and let it simmer for 10-12 minutes, or until the potatoes are tender.
Stir in the minced chipotle peppers, smoked paprika, dried oregano, salt, and black pepper.
Gently fold the shrimp into the chowder and let it simmer for an additional 5-7 minutes, or until the shrimp are cooked through and opaque.
Pour in the heavy cream and stir to combine. Let the chowder simmer for a few more minutes, allowing the flavors to meld and the chowder to thicken slightly.
Ladle the Smoky Chipotle Shrimp Chowder into bowls and garnish with freshly chopped cilantro. Serve hot, accompanied by crusty bread or oyster crackers.