Prepare Garlic Yogurt Base: In a medium bowl, whisk together room-temperature Greek yogurt, finely grated garlic, 1 tbsp olive oil, and 1/4 tsp fine sea salt until silky smooth. Divide between two wide, shallow bowls and spread into swooping wells using the back of a spoon.

Simmer Poaching Water: Fill a medium saucepan with 3 to 4 inches of water. Bring to a gentle simmer over medium heat until small bubbles form at the base. Stir in 1 tbsp white vinegar. Crack each cold egg into a small ramekin or fine-mesh strainer.

Poach the Eggs: Stir simmering water in a circle to create a gentle vortex. Slip an egg into the center. Cook gently for 3 minutes until the whites are fully set and the yolks remain soft and runny. Remove with a slotted spoon and drain on paper towels for 15 seconds.

Sizzle Aleppo Chili Butter: In a small skillet or butter warmer over medium heat, melt 3 tbsp butter with 1 tbsp olive oil until foaming. Add Aleppo pepper flakes and cumin; swirl for 30 seconds until fragrant, nutty, and bright crimson. Remove immediately from heat.

Assemble & Serve: Nest two warm poached eggs onto the garlic yogurt bed in each bowl. Spoon sizzling Aleppo chili butter over eggs and yogurt. Scatter with fresh dill, mint, and flaky sea salt. Serve immediately with warm crusty sourdough bread.