In a small pan over medium-low heat, melt the butter and olive oil. Add garlic, Aleppo pepper, red pepper flakes, salt, coriander, and cumin. Cook for 2 to 3 minutes until it turns a deep orange/red color. Remove from heat and set aside.
In a bowl, mix together the Greek yogurt, olive oil, lemon zest, dill, black pepper, and salt until creamy and thick. Set aside.
Heat a pot of water over medium heat until it simmers (small bubbles along the edges, not boiling). Add vinegar to the water.
Crack one egg into a small bowl, then gently drop it into the water. Cook for 2 to 3 minutes until the whites set (2 minutes for an extra runny yolk). Use a slotted spoon to remove the egg from the water. Repeat with the remaining eggs.
To assemble, spread yogurt on the bottom of a plate or bowl. Place poached eggs on top (two per plate). Drizzle chili oil over the eggs and garnish with chopped mint and chives. Enjoy!