Mix the 1 cup of flour with the 1 tablespoon of Cajun Seasoning until thoroughly combined. Coat the squirrel meat on all sides with the seasoned flour.
Heat a large pan (that has a lid) or Dutch oven over medium heat. Add the cooking oil.
Once the oil is hot and starts to shimmer, add the squirrel pieces. Cook them on each side for around minutes or until golden brown. Remove the squirrel from the large skillet and set aside.
Add the sausages to the pan and cook until browned, around 3 minutes. Add the onions and bell peppers to the pan. Season them with salt and cook for around 2 to 3 minutes or until slightly tender.
Add the mushrooms and garlic and cook for another 2 minutes while stirring and ensuring that the garlic doesn't burn.
Add the beer to the pan and scrape up any bits that have stuck to the bottom of the pan. Add the squirrel pieces along with the bay leaf and dried thyme to the pan. Pour the chicken stock over the squirrel. Cover the pan with a lid and bring the stew to a slow simmer.
Cook at a slow simmer between 1 and 2 hours or until the squirrel meat is fork tender but not falling off of the bone. Remember that the times may vary depending on the size and age of the squirrels. Keep and eye on the liquid levels and add a little chicken stock if needed.
Gently remove the squirrel pieces from the pan and set them aside.
In a small bowl mix the melted butter and flour together until you have a smooth paste. Pour the paste into the hot liquid in the pan while whisking until smooth and combined. Bring to a slow simmer and add the squirrel back to the pan. Cook at a low simmer for around 3 to 5 minutes. If the mixture is too thin, mix another batch of flour and butter together and add a little bit at a time to the pan until it has reached your desired thickness. If the mixture is too thick, add a little more chicken stock or hot water to thin it out.
Garnish with green onion and season with Cajun spice, kosher salt and black pepper to your liking.