Combine the Greek yoghurt, finely chopped or crushed garlic, lemon zest, chopped dill and a pinch of salt in a bowl and mix until smooth. Spread the yoghurt onto your serving plate and allow it to come to room temperature while you prepare the eggs.
Bring the Water to Temperature
Fill a saucepan three-quarters full with water and place it over medium heat. Bring the water to a boil, then reduce the heat to a gentle simmer so it is lightly bubbling rather than rapidly boiling.
Prepare the Eggs for Poaching
Crack one egg into a fine sieve to remove the thinner, watery whites, then transfer it carefully into a small bowl. Repeat this process with the second egg.
Poach the Eggs
Stir the simmering water gently with a spoon to create a whirlpool in the centre, then carefully drop one egg into the middle. Cook for 2½ minutes for a soft, runny yolk before removing with a slotted spoon and draining on kitchen paper. Repeat with the second egg.
Make the Smoky Chilli Butter
Melt the butter and extra virgin olive oil together in a small pan over low to medium heat. Once melted and gently bubbling, stir in the chilli flakes and smoked paprika and allow them to infuse for 30–60 seconds before removing the pan from the heat.
Toast the Sourdough
Heat a frying pan with a drizzle of olive oil and toast the sourdough slices on both sides until golden and crisp.
Assemble and Serve
Place the poached eggs on top of the garlic yoghurt base, spoon over the hot chilli butter and serve immediately with the toasted sourdough.