Stir together the yogurt, olive oil and chives in a medium bowl, and then season with the salt and pepper.
Melt the butter in a small pot over medium heat, stirring constantly until it turns a light golden brown color. Stir in the chile flakes and set the pot aside.
Place a deep pot of water over high heat to poach the eggs. Stir in 2 tablespoons of white vinegar for every 8 cups of water in the pot (this will help to cook the eggs and give them a better shape).
Bring the water to a boil, and then run a metal spoon around the edge of the pot to create a whirlpool. Quickly crack and carefully drop the eggs one by one into the middle of the pot. Reduce the heat to a simmer and cook the eggs until they are firm but give a bit (this will give a runny yolk), about 3 minutes. Remove the eggs with a slotted spoon, allowing the excess water to drain from each egg.
Put an equal amount of the yogurt mixture into the bottom of 4 bowls, making a slight indention in the middle for the eggs to sit. Put 2 poached eggs on top of the yogurt in each bowl and pour the chili butter on top. Serve with grilled sourdough bread and Quinoa Hash on the side.
Preheat the oven to 325 degrees F.
Shred the potatoes in a food processor with the grater attachment, and then squeeze with your hands to drain off the excess liquid. Mix together the potatoes, quinoa, cumin and salt in a large mixing bowl.
Spread oil over a baking sheet and lay a sheet of parchment paper on top. Oil the parchment paper, and then press the quinoa mixture into the baking sheet. Cover with a layer of oil, another sheet of parchment paper and another baking sheet. Bake for 20 minutes, rotating the baking sheet halfway through. Refrigerate until cold, and then cut into desired shapes.
Before serving, cook the hash browns in a pan with a generous amount of oil until golden brown and crispy. Transfer to paper towels to drain the excess oil and serve hot.