Set aside 1 whole thyme sprig.
Stack bay leaf and remaining thyme sprigs in a bunch; tie reserved thyme around the bunch and secure with a knot to make bouquet garni.
Pat shrimp dry with a paper towel and season all over with half of the spice mix, 1 teaspoon salt, and black pepper as desired.
Heat 2 tablespoons canola oil in a large pot over medium-high heat.
When oil is shimmering, add shrimp and cook, stirring occasionally, until opaque and just pink, 4-6 minutes total.
Using a slotted spoon, transfer shrimp to a plate and set aside. Wipe pot clean for the next step.
Place pot from shrimp over medium heat and add 2 tablespoons canola oil. When oil is shimmering, add bouquet garni, onion, and garlic.
Sauté, stirring, until onion begins to soften, about 3 minutes.
Add bell peppers, celery, and remaining spice mix and cook, stirring, until vegetables begin to soften, about 3 minutes more. Season with .5 teaspoon salt and black pepper as desired.
Increase the heat under the pot with aromatics to medium-high, and add potatoes. Cook, stirring, until softening, 5 minutes. Add tomato paste and stir to fully coat vegetables, 1-2 minutes more.
Add corn and vegetable stock to the pot, then add enough water to just cover potatoes (this ensures they're fully submerged and can cook through evenly and completely). Stir to combine. Increase heat to high and bring to a boil, then reduce heat to medium-high and simmer until soup has reduced and potatoes are tender when pierced with a knife tip, 5-7 minutes.
Reduce heat under pot to medium. Return cooked shrimp to pot and stir to warm through, 3-4 minutes. Remove and discard bouquet garni, then taste and add salt and black pepper as desired.
Ladle Cajun shrimp and corn chowder into roomy serving bowls, garnish with parsley, and dig in!