CREAMY MUSHROOM TOAST WITH SOFT EGG & GRUYÈRE

Ingredients

• 2 tablespoons unsalted butter, more as needed
• Olive oil
• 8 ounces mushrooms, ends trimmed and sliced into even pieces
• 3 cloves garlic, smashed
• 3 large sprigs of thyme
• ½ shallot, finely minced, about 2 tablespoons
• Kosher salt
• Freshly ground black pepper
• Sherry vinegar
• 3 tablespoons crème fraîche
• 2 thick slices sourdough or country bread, toasted in a pan with butter
• Handful of arugula, tossed with olive oil, lemon juice and salt
• 2 soft-poached eggs, topped with flaky salt and black pepper
• Gruyère cheese, shaved