Savory crepes with mushroom ragout and eggs

Remove the stems of button mushrooms and thinly slice all mushrooms. Chop bigger slices in two or three parts.In a large pan pr skillet, heat olive oil over medium-high heat. Add shallots and cook until tender, stirring occasionally, for about 10-15 minutes. Add the garlic, stir and cook for another minute.Add the mushrooms and cook until they release all the liquid, stirring occasionally.Add the vegetable stock and thyme and cook for 5-10 minutes, until most of the liquid evaporates.Add the cream and cook for another minute.Remove mushrooms from the stove, stir in the parsley. Taste and add a pinch of salt and a grind of black pepper, or more to taste.Preheat the oven to 250°C (480°F) and place a rack in the lowest row in your oven.Line a small square baking dish with parchment paper, whisk one egg in a small bowl and set aside.Take two crepes and put one over the other, so they partially overlap. Spread two large tablespoons of mushroom ragout in the center. Sprinkle with 2-3 tablespoons of grated cheese.Brush all corners of the crepes with the whisked egg.Gently roll the crepes in a log (not too tightly!), then roll again in a coil shape. Place in the baking dish and brush with egg.Repeat with the remaining 6 crepes and make 3 more crepe rolls.Gently pat down the crepe rolls, so they flatten on the surface. Crack an egg onto each roll. Generously sprinkle with more cheese.Bake for 10-15 minutes or until you see the egg whites have turned from translucent to white. The yolk should remain runny. Often the yolk hardens on the surface but is still runny in the center. The crepes will be crispy on the outside.Sprinkle with chopped parsley (about a tablespoon) and serve immediately.