Prepare the fish: Pat the fish dry and season with salt and Cajun seasoning. The fish will come to temp while you're doing the next steps.
Start the grits: In a saucepan, bring the chicken stock to a boil. Whisk in the grits, reduce heat to low, cover and simmer gently for about 20 minutes. Stir occasionally until the stock is fully absorbed and the grits are tender. They tend to stick to the bottom of even a non-stick pot, so scrape up off the bottom with a wooden spoon. While the grits are simmering, make the succotash.
Make the succotash: In a clean skillet, melt the butter or oil over medium heat. Add the onion and red bell pepper, sautéing 4-5 minutes until softened. Add the garlic and cook 30 seconds. Stir in the lima beans, black-eyed peas, and chicken broth. Simmer 5-8 minutes until the limas are tender and most of the liquid has reduced. Season with salt and pepper. Turn off heat and cover to keep warm.
Finish the grits: After all the stock is absorbed, stir in the white cheddar until melted. Season with salt to taste and a small pat of butter if desired. Cover and set aside.
Cook the fish: Heat a skillet over medium-high with the oil or butter. Sear the fish for 3-4 minutes per side, or until golden brown and just cooked through. Transfer to a plate and set aside. (Don't leave them in the pan or they might overcook from the residual heat.)
Finish and assemble: Spoon a generous portion of the white cheddar grits onto each plate or shallow bowls. Place a seared snapper fillet alongside or partially overlapping the grits. Add a scoop of succotash over or beside the fish. Garnish with the chopped parsley, a lemon slice or wedge, and shaved Parmigiano Reggiano. Serve immediately.