Add the potatoes and turnips to a large pot, cover completely with water (add a few big pinches of salt), then bring to a boil. Reduce to a simmer and cook the vegetables until they are easily pierced with a fork, about 25-30 minutes.
Meanwhile, add a small drizzle of olive oil to a large dutch oven or heavy-bottomed pan. Add the bacon and cook over medium heat, until the fat is rendered and the bacon is crispy. Remove the crisped bacon from the pot, reserving the rendered fat.
Add the sliced onion to the rendered bacon fat and saute for 3-4 minutes, until the onion softens slightly. Add the cabbage to the pot and saute for 12-15 minutes, until the cabbage is very tender. Season with salt and pepper.
Once the potatoes and turnips are cooked, drain well, then return them to the pot. Add the sour cream and a pinch of salt and pepper. Using a potato masher, coarsely mash them, then add to the pot with the cabbage and onion. Stir in the crisped bacon (reserve some for garnish) and season with salt and pepper to taste.