Preheat the oven to 375°F (190°C).
In a small bowl, combine paprika, garlic powder, onion powder, oregano, thyme, cayenne pepper, black pepper, and salt to create the Cajun spice mix.
Pat the turkey breast dry with paper towels. Rub 1 tablespoon of olive oil evenly over the turkey breast.
Generously coat the turkey breast with the Cajun spice mix, pressing it into the skin and meat.
In a large mixing bowl, toss the carrots, red potatoes, red bell pepper, yellow onion, and minced garlic with the remaining 1 tablespoon of olive oil and a pinch of salt and black pepper.
Place the seasoned turkey breast in the center of a large roasting pan or baking dish.
Arrange the mixed vegetables evenly around the turkey breast in the pan.
Roast in the preheated oven for about 1 hour and 15 minutes, or until the internal temperature of the turkey breast reaches 165°F (74°C) when measured with a meat thermometer.
Halfway through cooking (around 35-40 minutes), stir the vegetables to ensure even roasting.
Once cooked, remove the turkey breast from the oven and let it rest for 10 minutes before slicing.
Transfer the turkey slices and roasted vegetables to a serving platter and garnish with chopped fresh parsley.