Preheat the oven to 400 degrees.

In a large (12-inch) ovenproof skillet, heat 2 TBSP oil over medium-high. Add half the mushrooms, season with salt and pepper and cook, undisturbed, until browned, about 3 minutes. Stir the mushrooms, then continue to cook until browned all over, about 3 minutes longer. Transfer to a medium bowl.

Repeat with the remaining 2 TBSP oil and the remaining mushrooms; transfer them to the medium bowl.

Reduce the heat to medium and add the butter to the skillet. Once the butter is melted, add the onion and carrots and cook until starting to soften, about 5 minutes.

Add the garlic and cook for 30 seconds, until fragrant. Add the tomato paste and cook 1 minute longer. Stir in the flour and cook 1 minute longer.

Then add the kale, wine, broth, thyme, and soy sauce. Season with salt and pepper, and cook for about 3 minutes, until the kale is starting to soften.

Stir in the cream.

Add the mushrooms back to the skillet and stir to combine. Season with additional soy sauce, salt, and pepper, to taste.

Roll the puff pastry out so that it’s large enough to cover the skillet, and use a knife to form it into a circle shape.

Place the puff pastry on top of the mushroom mixture, and crimp the edges using the tines of a fork, if desired. Create a stripe pattern in the puff pastry by gently running a paring knife over the top without fully cutting through.

Whisk the egg with 1 TBSP heavy cream, then lightly brush the egg wash over the top of the puff pastry.

Set the skillet on top of a baking sheet and bake until the puff pastry is puffed and golden, about 30 minutes. Let sit for 10 minutes before enjoying.