Create a small double boiler by filling a medium saucepan with about 2 inches of water and bringing it to a simmer.
Once the water is simmering, mix together the yogurt, garlic, dill, and salt in a medium heat-proof bowl and place it on top of the saucepan of simmering water, ensuring that the bottom of the bowl does not touch the water.
Cook, stirring constantly, until the mixture is of the consistency of lightly whipped cream – thickened slightly but also warmed through. Remove the bowl from the heat and set aside.
For the Spiced Butter Drizzle:
In a small saucepan, melt the butter over medium heat. Swirl the pan until the butter lightly browns and smells nutty. Remove the pan from the heat and stir in the olive oil, red pepper flakes, and dill. Set aside.
Poach your eggs to desired doneness (I do two per person).
Spoon the whipped yogurt mixture into the bottom of two serving bowls and top with the poached eggs. Drizzle the spiced butter mixture over top, garnish with additional dill, and serve immediately with toasted bread or naan on the side for dipping.