Heat the oven to 195°F (90°C).

Carefully separate the eggs, reserving the yolks. Place the yolks in a small oven-safe ramekin or heatproof bowl, ensuring they stay whole and do not touch each other. Add the garlic cloves, salt, and thyme.

Pour in the olive oil to fully submerge the yolks. Transfer the ramekin to the oven and bake for 50 minutes, until the yolks are lightly set on the outside but still soft and creamy inside.

Serve warm over toasted sourdough, swirl into hot pasta, or spoon onto a salad. Use immediately, or store in the oil for up to 24 hours in the refrigerator. Bring to room temperature before serving.