In a large pot, melt butter over medium heat.
Add finely chopped shallot and sauté until translucent, about 3-4 minutes.
Stir in minced garlic and cook for an additional 1 minute until fragrant.
Sprinkle gluten-free flour over the mixture and stir continuously to form a roux, cooking for 2 minutes.
Gradually pour in chicken stock and seafood stock, whisking to avoid lumps.
Add tomato sauce, sliced deseeded jalapeño, bay leaves, dried oregano, salt, dried thyme, and white pepper to the pot.
Bring the soup to a gentle boil, then reduce heat and let simmer for 15 minutes to develop flavors.
Add peeled and deveined shrimp to the simmering soup and cook until pink and opaque, about 3-5 minutes.
Remove the bay leaves and discard.
Squeeze the juice of half a lime into the soup and stir well.
Serve the soup hot over cooked white rice.
Garnish with jalapeño rings, fresh cilantro, and lime wedges on the side.