Before you start, make sure your skillet is big enough to accommodate everything. If it isn’t, pare the recipe down slightly to fit. Also, prepare the pastry: roll it out slightly, to even it out, and cut it to fit your pan (with an inch or two overhang). Place it on a baking sheet and keep it in the fridge while you cook.
Preheat the oven to 400F.
Get the skillet nice and hot over high heat on the stove, then add 2 Tbsp butter and the sliced onions. Cook, stirring frequently, until they’ve browned and caramelized a bit (about 8 minutes).
Reduce the heat to medium, then add the remaining butter, carrots, and celery. Cook for 3-4 minutes before adding the chopped chanterelles.
Let this mixture cook for 5-8 minutes, until the mushrooms are all softened and some of the moisture has evaporated before sprinkling the flour over the vegetables, and stirring to combine. Stir continuously, scraping the bottom of the pan, for 3 minutes.
Gradually pour in the chicken broth, using your spoon to vigorously scrape the bottom of the pan (to get all the flavorful bits off of the pan!), then add the chicken and bring the mixture to a simmer.
Season with salt and pepper, remove from the heat, and stir in the chopped kale until mostly wilted. Add the half & half, stirring again to combine.
At this point, cut a few vents in your puff pastry, and (work quickly so it doesn’t warm up too much before going into the oven) lay it over top of the skillet.
Put it immediately in the oven and bake for 30-40 minutes, or until the pastry is golden and the pot pie is bubbling.