In a medium skillet over medium heat, melt the butter. Add the leeks and salt, cooking for 8–10 minutes, stirring often, until softened but not browned. If they start to brown, reduce the heat.
Stir in the flour and cook for 1 minute. Add the stock, stirring, and simmer for 2 minutes, until it thickens slightly.
Turn off the heat and stir in the chicken, sour cream, Dijon, tarragon, thyme, and pepper. Taste for salt and adjust as desired. Chill until fully cold or at least room temperature, about 30 minutes.
Preheat the oven to 400˚F and line two sheet pans with parchment paper. If you have enough sheet pans, we like to stack a second sheet pan underneath each one so the bottoms of the pastry don't brown too quickly.
On a floured surface, roll each sheet of puff pastry to about 13×13 inches. We use a 3 ½-inch circular cookie cutter for the bottoms – cut 9-10 circles from one sheet of puff pastry (or as many as you can fit). On the other sheet of puff pastry, we use a ~4-inch cookie cutter for the tops. Again, cut out 9-10 circles, or as many as you can fit.
Mound 2 tablespoons of cooled filling on each bottom circle of puff pastry, leaving a border around the edges. Brush egg wash all around the border. Top with the slightly bigger top circle, pressing firmly all the way around the edges to make sure it's well sealed and there are no air pockets. Use a fork to firmly crimp the edges together. Optional: use the 3 ½-inch cookie cutter to re-trim the circle so it looks neat!
Brush the tops of each pastry with a thin, but even layer of egg wash. Using a sharp paring knife, poke several holes in the top so steam can escape. To decorate with thyme leaves, dip the sprig in some egg wash, then press it onto the top of the pastry.
Bake for ~22 minutes, rotating the pan at 15 minutes, until the pastries are deep golden on both the top and bottom. Cool for 5 minutes before serving.