Cajun Roasted Turkey and Gravy

Ingredients

• 2 tablespoons Garlic Powder
• 2 tablespoons paprika
• 1 tablespoon dried oregano
• 1 tablespoon dried thyme
• 1 tablespoon freshly ground black pepper
• 1 tablespoon onion powder
• 4 teaspoons cayenne pepper
• 6 quarts cold water
• 1 12-ounce bottle amber ale beer (room temperature)
• 1 cup kosher salt
• 1 cup packed brown sugar
• 3 each rosemary sprigs (divided)
• 1 Turkey 14- to 16-pound whole turkey
• 3 each celery stalks (coarsely chopped)
• 2 each green bell peppers (seeded, coarsely chopped)
• 2 each yellow onions (coarsely chopped)
• 3/4 cup unsalted butter (divided, 1 1/2 sticks)
• 4 cups homemade turkey stock or reduced-sodium chicken stock
• 3 each thyme sprigs
• 1/4 cup all-purpose flour