Combine peppers, onions, and celery in a bowl and have ready next to the stove. In a large heavy skillet (cast iron is best) heat oil until it just begins to smoke. Gradually add flour, whisking constantly. Continue whisking constantly and cook over medium to medium-high heat until roux is dark brown and very fragrant. Add vegetable mixture and stir with a wooden spoon, continuing to cook, for 2 minutes. Add salt and dry seasonings and garlic and stir to combine, cooking for another 1 to 2 minutes, then remove pan from heat.
Place shrimp stock in a large Dutch oven or stockpot and bring to a gentle boil. Gradually add roux mixture to boiling stock, whisking constantly, until completely incorporated and dissolved. Return to a boil and add the andouille, then reduce to a simmer and cook for 15 minutes. Taste and adjust seasoning if necessary, then add shrimp and turn off heat. Let gumbo sit for 5 minutes to allow shrimp to cook, then serve immediately over a scoop of plain white rice.
Note: You can do everything in this recipe up to the point of adding the shrimp beforehand; bring gumbo up to a boil before adding shrimp to serve.
Cooking the roux can be tricky. For safety's sake, wear good oven mitts while whisking (roux can cook to nearly 400 degrees F!) and be very careful not to let it burn on the bottom. If black bits show up in the roux before it is done, you must start over, boo-hoo. If the roux starts to smoke, remove it from the heat for a few minutes and keep whisking?remember that the pan will retain a lot of heat that will continue to cook the roux even off the flame. This is not a quick project! Your patience will be rewarded with a rich, delicious gumbo.
Peel and de-vein the shrimp and reserve the shells. Refrigerate the shrimp until needed. In a saucepan or stockpot, heat the oil over medium-high heat. Add the onion, carrot, and celery and cook until slightly softened, about 5 minutes. Then, add the shrimp shells and cook, stirring constantly, until shells are pink and fragrant. Add the wine and cook until reduced by half. Add water to the pot to just past the level of the shrimp shells and add peppercorns, bay leaf, and thyme. Bring to a boil and immediately reduce to a simmer. Skim impurities (i.e., scum) from top of stock and simmer for approximately 30 to 45 minutes. Strain stock and reserve.