Finely grate the garlic into the yoghurt, stir together with the dill, salt and lemon juice, and set to one side.
Bring a large pan of water up to a simmer, add the vinegar, swirl the water, and drop the 2 eggs into it, one at a time. Poach for 4–5 minutes, until the whites are set.
While the eggs are poaching, melt the butter in your smallest pan. Take it to the point where it is just starting to brown: it should smell nutty, but the colour won’t really have changed yet. Stir in the Aleppo pepper, and set to one side.
Divide the yoghurt between two dishes, drain the eggs and set them on top of the yoghurt, dress with the butter and garnish with extra dill. Serve with warm, soft bread.