1Preheat oven to 425 degrees F (220 degrees C). Spread potato nuggets on a baking sheet in a single layer.
2Bake in the preheated oven until browned and crisp, 20 to 25 minutes. Transfer to a large bowl; season lightly with salt.
3Mix pulled pork and barbeque sauce together in a bowl until pork is evenly coated.
4Whisk sour cream and smoked paprika together in a small bowl.
5Melt butter in a saucepan over medium heat. Whisk in flour until a paste forms, 2 to 3 minutes. Whisk in milk until no lumps remain. Cook and stir until sauce thickens enough to coat the back of a spoon, about 5 minutes. Remove from heat; whisk in Cheddar cheese until melted. Season sauce with salt and pepper.
6Drizzle Cheddar cheese sauce over potato nuggets. Cover with pulled pork mixture and dollops of sour cream. Top with pinto beans, roasted peppers, green onion, and thyme.
Substitute roasted pimentos for the red bell peppers if preferred.