Preheat the air fryer to 350°C.
Place the butter in a medium mixing bowl. Melt it in the microwave for about twenty seconds. When melted, add the white wine, garlic, thyme, pepper, and salt. Stir with a teaspoon until the salt is dissolved.
Take the mushrooms, and clean them one by one. With a damp cloth, rub the surface of the portobellos, being careful not to scratch the skin. Then, with a soft bristle brush, brush the bottom of the mushrooms. Gently pull off the stem.
Then, using a kitchen brush, brush the portobellos with plenty of dressing. They must be well moistened.
Put them into the air fryer with the gills facing up. Cook them for five minutes.
Flip them over and cook for two more minutes. When ready, they will be well cooked and crispy.
To prepare the sauce, finely chop onion, pickles, capers, and parsley. Pour the chopped vegetables into the bowl with the mayonnaise and stir until all the elements are well integrated. You can serve the portobello with a little sauce on top. Or, just place the sauce on the side.