Remove any dirt or debris from the mushrooms with your hands, or small soft brush. (do not use water!). Slice the stems into enough rounds so that each person has 5 or 6. Keep the caps for another dish.
Drain the capers and pat them dry with a clean tea towel or paper towel. Heat about a tablespoon of ghee (or coconut oil) in a large skillet over medium-high heat. Add the capers and fry until split and crisp – about 2-3 minutes. Remove from pan and set aside.
Add more ghee (or coconut oil) to the same skillet over medium-high heat. When hot, add the sliced mushroom stems, a sprinkle of flaky salt, and cook on one side until golden, about 5-7 minutes. Then flip and cook on the other side until golden. Work in batches or use separate skillets – if you crowd the mushrooms they will steam each other and get soggy. That is not what we’re after!
While you’re cooking the mushrooms, place the pesto in a small saucepan, add a touch of water to thin, if desired, and warm over low-medium heat. Do not boil!
To serve, place about ¼ cup / 60ml of the warm pesto in the bottom of a dish, spreading it out to make an indent in the center. Place 5 or 6 mushroom stems in the pesto, then top with the fried capers and toasted hazelnuts. Drizzle with olive oil and a few grinds of black pepper. Garnish with parsley and serve.