Preheat the oven to 200°C (180°C fan-forced). Heat a large, deep cast-iron skillet over high heat. Pour in 2 tablespoons of olive oil and add the field mushrooms. Cook for about 5 minutes, stirring frequently, until they develop a golden color and their liquid has fully evaporated. Transfer them to a heatproof bowl. Repeat this process with the button and Swiss brown mushrooms, adding another 2 tablespoons of oil and cooking for 5 minutes until golden and dry. Transfer to the bowl.

For the final batch, heat the remaining oil in the skillet and add the portobello mushrooms. Cook for another 5 minutes, stirring occasionally, until they turn golden and their moisture has cooked off. Once done, transfer them to the bowl with the other mushrooms and set aside.

Reduce the heat to medium and melt the butter in the same pan. Add the sliced red onion and stir continuously for about 2 minutes, allowing it to soften and develop a light golden hue. Pour in the white wine, followed by most of the thyme leaves and the extra sprigs. Let the mixture simmer gently for about 3 minutes, stirring occasionally, until the wine reduces by two-thirds.

Sprinkle in the flour, stirring constantly for 1 minute to remove any raw taste. Gradually pour in the thickened cream, reserving 2 teaspoons for later, then add the crushed garlic. Return all the cooked mushrooms, along with any juices that have collected in the bowl, back into the pan. Stir well to combine everything, bringing the mixture to a gentle simmer before removing it from the heat. Generously season with salt flakes and freshly ground black pepper—mushrooms can handle bold seasoning.

Lay the puff pastry over the mushroom filling, trimming away any excess. Prick a few small holes in the pastry using the tip of a knife to allow steam to escape. Lightly brush the surface with the reserved 2 teaspoons of cream for a golden finish.

Place the skillet in the preheated oven. To prevent spills, position a large baking tray on a lower rack to catch any sauce that may bubble over. Bake for 35 to 40 minutes, or until the pastry is golden brown, puffed, and crisp. Once baked, remove from the oven and let it rest for 5 minutes before serving.

Garnish with the reserved thyme leaves and serve with radicchio leaves on the side, if desired.