To prepare the braised beef short ribs, season the short ribs on all sides with the salt and pepper. Let stand at room temperature for 1 hour.

Preheat the oven to 350°F.

In a heavy-bottomed ovenproof pot that will fit the short ribs in one layer, warm the olive oil over high heat. When the oil looks “wavy” hot, add the short ribs, meaty side down, and sear for 4 to 5 minutes per side. Transfer to a plate.

Reduce the heat, add the onion, carrots, garlic and thyme to the pot and cook, stirring occasionally, until starting to soften, 3 to 4 minutes. Return the short ribs, meaty side up, to the pot. Add the wine and deglaze the pot, stirring to scrape up the browned bits. Add the broth and bring to a simmer. Cover the pot, transfer to the oven and cook until the meat is fork-tender, about 2 1/2 hours.

To assemble the puff pastries, break the short rib meat into small pieces and place in a bowl. Add the braising sauce and chives. Season with a little salt and pepper and stir to combine.

On a floured surface, gently roll out the puff pastry into 4-inch  rounds. Using a fork, prick holes all over the surface of the rounds. Place the short rib mixture in the center of the rounds, dividing evenly. 

In a small bowl, whisk together the egg and water to make an egg wash. Lightly brush the edges of the rounds with some of the egg wash and fold over one side to create a half-moon. Press the edges to seal and refrigerate the filled pastries for at least 1 hour. Refrigerate the remaining egg wash.

Preheat the oven to 375°F. Line a baking sheet with parchment paper.

Remove the pastries from the refrigerator and brush the tops lightly with the egg wash. Place on the prepared baking sheet, transfer to the oven and bake until the pastries are golden brown, 12 to 15 minutes.