Preheat the oven to 300°. In a large nonstick skillet, heat 2 tablespoons of the oil until shimmering. Add half of the pierogies and cook over high heat until lightly browned, about 2 minutes per side. Transfer the pierogies to a large rimmed baking sheet and cover with foil. Repeat with the remaining oil and pierogies; keep hot in the oven.
Wipe out the skillet and add 2 tablespoons of the butter. Once it has melted, add the bacon and cook over moderate heat, stirring occasionally, until golden brown and crisp, about 7 minutes. Add the remaining 2 tablespoons of butter and the onion and cook over moderately low heat until the onion is softened, about 5 minutes. Stir in the cabbage, season with salt and pepper and cook, stirring occasionally, until the cabbage is very tender, about 15 minutes. Stir in the hot and sweet paprikas and cook, stirring, until fragrant, about 3 minutes. Add the yogurt and hot water and stir until smooth and creamy. Add the pierogies and gently toss with the sauce. Transfer the pierogies to a warm platter, sprinkle with the parsley and serve right away.