Preheat the oven to 450 degrees F (230 degrees C).
Spread potato nuggets in a single layer on a baking sheet.
Bake in the preheated oven until tots are golden brown, about 25 minutes.
Meanwhile, whisk mayonnaise, sour cream, 1 tablespoon truffle oil, garlic, lemon juice, and pepper in a mixing bowl. Set aioli aside.
Remove tots from the oven and transfer to a large bowl. Let cool for 5 minutes. Drizzle with remaining 3 tablespoons truffle oil; toss to combine. Add Parmesan cheese and parsley; toss to combine. Serve tots with reserved aioli.