Whisk together the flour, Schwartz Cajun Seasoning, eggs, and milk in a large mixing bowl. Season and set aside.
Toss the peppers, onion, sausages, and thyme in 12 tbsp vegetable oil in a medium, high-sided nonstick roasting tray (about 34 x 24 x 5cm) and roast for 15 minutes, tossing occasionally, until gently golden.
Drizzle the remaining 1 tbsp oil over the hot tray before pouring the batter over the vegetables and sausage. Return to the oven and cook for 25-30 minutes, or until golden and risen, making sure not to open the door too soon.
Make the gravy in the meantime. In a medium saucepan, heat the oil and cook the onion for 15 minutes, turning periodically, until tender and transparent. Cook, stirring constantly for 2 minutes after adding the Schwartz Cajun Seasoning and plain four, then gradually whisk in the veggie stock. Simmer for 10-15 minutes and season with salt and pepper to taste.
Serve the Cajun toad-in-the-hole with the onion gravy and steamed tenderstem broccoli.