Preheat oven to 425°F.
In a small bowl add Cajun seasoning, black pepper, rosemary, cayenne, salt, garlic powder and onion powder. Mix well. Set aside.
Add oil and butter to a small sauté or frying pan.
Place over medium heat.
When butter has melted and mixture begins to boil around the edges, Add the spice mixture. Stir to combine.
Remove pan from heat. Set aside to allow the flavors to "infuse" into the oil mixture.
Place about 1/3 of the still frozen tater tots in a medium to large bowl with a sealable top.
Drizzle in about 1/3 of the spice oil mixture.
Place the top on bowl (or cover tightly with plastic wrap) and vigorously toss the tater tots to coat with fully with sauce.
Pour cover tots out of bowl onto a baking sheet.
Repeat with another 1/3 of each and again until all of the tater tots are covered and on the baking sheet.
Drizzle any spice oil mixture remaining in both bowls over tots.
Place sheet in preheated oven. Bake for 25 to 35 minutes or until tots are very crispy.
Remove from the oven.
Taste. Add more salt and pepper, to taste, if needed.
Serve hot with various Dipping Sauces (See Box Below for Links to Recipes).