Cook the Vegetables: In a large pot, melt 3 tablespoons of dairy-free butter over medium heat. Add the chopped onion, diced red bell pepper, and minced garlic. Sauté until the onions become translucent and the peppers are soft about 5-7 minutes.
Add the Corn and Seasonings: Stir in the corn kernels, 2 tablespoons of tomato paste, 1/2 teaspoon of smoked paprika, and 1 tablespoon of Cajun seasoning. Cook for another 2-3 minutes, allowing the spices to become fragrant.
Create the Base: Sprinkle 1/4 cup of gluten-free flour over the vegetables and stir well to combine. This will help thicken the chowder. Gradually pour in the 4.5-5 cups of chicken or vegetable broth while stirring to avoid lumps. Bring the mixture to a gentle boil, then reduce the heat and let it simmer for about 10-12 minutes, allowing the flavors to meld.
Add the Coconut Milk: Stir in the 14 oz can of coconut milk (or dairy-free milk) to the pot. Continue to simmer for another 5 minutes.
Blend: Using an immersion blender, blend the soup to thicken it up. Make sure not to blend until smooth, just a quick flash blend. You still want some veggies to be whole.
Add Shrimp: Add the peeled and deveined shrimp to the pot. Cook for about 3-4 minutes, or until the shrimp turn pink and are cooked through.
Season and Serve: Taste the chowder and adjust the seasoning with salt and pepper to your liking. Remove the pot from heat and let it sit for a few minutes to thicken slightly. Ladle the chowder into bowls, garnish with 2 tablespoons of chopped fresh parsley, and serve hot.