Peel potatoes and wash. Use a mandolin, or food processor with the grater attachment, to finely shred potatoes. Place in a kitchen towel and squeeze dry.
Take a 9-inch oven proof skillet and add bacon and sliced shallots. Set over medium heat and render fat, 4 to 5 minutes. Shallots will caramelize. Using a slotted spoon, remove the bacon and shallots and put in a large mixing bowl (reserve the bacon fat and pan) with potato slices, egg white, green onions, and thyme leaves and season well with salt and pepper. Toss to combine. Spoon mixture into the hot pan with the bacon fat. Pack it in well pressing down with a large spoon to compress the mixture a little. Drizzle the top with some extra-virgin olive oil and season with salt and pepper. When it starts to get golden brown and crispy around the edges flip the hash brown over and pop into the oven to bake for 15 minutes. Remove from oven and allow to cool slightly before running a knife around the edges and then inverting the potato onto a cutting board. Slice into wedges, garnish with chopped flat leaf parsley and serve.