In a small bowl mix together Greek yogurt through lemon juice. Cover with plastic wrap and let sit on the counter for up to an hour.
Preheat oven to 400 F
In a bowl mix together cherry tomatoes with a drizzle of olive oil, pinch of pepper and salt. Pour onto parchment lined baking sheet ensuring they are one layer.
Roast for 12-15 minutes or until the tomatoes have burst and are soft. Remove pan from oven and set aside.
Poach your eggs. With a slotted spoon remove to a plate with a paper towel once they are done cooking.
While eggs are poaching, toast your sourdough bread and butter if you wish.
Spread yogurt mixture on bottoms of two plates. Add a scoop of the tomatoes, two eggs on each plate, sliced sourdough bread, a sprinkle of black pepper, fresh mint, fresh dill and a drizzle of chile oil. Serve.