Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Clean and slice the cremini mushrooms, then toss them on the baking sheet with olive oil, minced garlic, fresh thyme, sea salt, and black pepper.
Roast the mushrooms for 15 to 20 minutes until they are tender and have developed a deep golden-brown color.
While the mushrooms roast, add the Greek yogurt to a small bowl, season with a pinch of salt, and spread it across the bottom of two serving plates.
Fill a wide saucepan with water and the apple cider vinegar, bringing it to a very gentle simmer over medium-low heat.
Crack each egg into a small ramekin and carefully slide them into the water one by one, poaching for about 3 minutes until the whites are opaque but the yolks remain soft.
Lift the poached eggs out with a slotted spoon, draining any excess water, and place two eggs onto each yogurt-lined plate.
Spoon the warm roasted mushrooms over the eggs and yogurt, then garnish with chopped fresh chives before serving immediately.