For the herb-bacon oil: Combine the olive oil and herbs in a bowl.
Heat the canola oil in a large cast iron skillet over medium high heat, add the bacon and cook until crisp, about 8 minutes. Transfer the bacon to a plate lined with paper towels to drain. Reserve the bacon pan drippings. Add the bacon to the herb oil, season with salt and pepper, and set aside.
For the hash: Heat the bacon drippings in the cast-iron skillet over medium heat. Add the onion and cook until soft, 4 to 5 minutes. Stir in the garlic and cook about 30 seconds.
Meanwhile, toss the sweet potatoes, Brussels sprouts and turkey in a large bowl and season with salt and pepper. Increase the heat to medium-high. Add the potato mixture, stir once to incorporate the onion and garlic, and then press firmly with a spatula against the bottom of the pan. Cook, pressing occasionally, until the bottom is browned and crispy, about 4 minutes, reducing the heat if the mixture starts to get too dark. (If the mixture seems dry, add some butter around the edges.)
Once the bottom is browned and crispy, flip the hash in chunks and press again to brown some of the top side.
For the poached eggs: While the hash is cooking, bring about 4 inches of water to a simmer in a deep skillet. Add the vinegar. Break each egg into a separate ramekin. Slip the eggs into the water and cook until the whites are set and the yolks still runny, about 4 minutes.
Right before the eggs are done, divide the hash among 4 or 6 plates. Remove each egg with a slotted spoon, blot it dry on a clean side towel, and put it on top of the hash. Drizzle each serving with some bacon-herb oil and serve.