Place the potatoes in a saucepan and add enough water to cover by about 1-inch. Place the pot over HIGH heat and add the salt. Bring the water to a boil then reduce heat to LOW and simmer for 3 to 4 minutes, or until the potatoes are just barely fork tender (don’t overcook as they’ll cook more later). Drain and set the potatoes aside.
Melt 2 tablespoons butter over MEDIUM heat. Add the chicken and 1 tablespoon of Cajun seasoning, and sauté until cooked through, about 5 to 6 minutes. Remove the pot from the heat and use a slotted spoon to transfer the cooked chicken to a plate and set aside.
Return the pot to MEDIUM-LOW heat and melt the remaining 3 tablespoons butter. Add the onions, celery and garlic and cook, stirring, for 3 to 4 minutes, or until tender. Then, add the flour and stir well to incorporate to create a roux. Cook, stirring, for 1 to 2 minutes more to lightly toast the roux. Lower the heat as needed to prevent the roux from browning.
Slowly add the chicken broth to the roux, a little at a time, stirring as you add it to smooth out any lumps. Increase the heat to MEDIUM or as needed to bring just to a bare simmer. Cook, stirring occasionally, until thickened, about 4 to 5 minutes.
Add the cream, milk, cooked potatoes, cooked chicken, corn, remaining 2 teaspoons Cajun seasoning, black pepper, cumin, parsley, and cilantro. Bring to a low boil, then reduce heat to LOW and let the chowder cook for 10 minutes, or until the potatoes and corn are tender. Should not boil but hot enough to continue thickening.
Remove from the heat and allow the chowder to rest for 5 to 10 minutes before serving.
Garnish with a small dollop of sour cream and a small amount of peppers.