Preheat the oven to 350 degrees F.
Bring a medium pot of water to a boil. Blanch the cabbage leaves for 15 seconds, and then rinse under cold water. Thinly shred the leaves and set aside.
Heat 1 tablespoon of the olive oil in a heavy saucepan over medium-high heat. Add the carrots, celery and onions and cook until softened, about 5 minutes. Add the garlic and cook 3 more minutes; season with salt and pepper. Transfer to a small bowl and reserve.
In the same saucepan, heat the remaining 1 tablespoon olive oil over medium-high heat. Add the pork and cook, breaking it up with a wooden spoon, until no pink remains. Add the cooked onion mixture, oregano and thyme, and stir to combine. Add the beef broth and bring to a simmer. Add the flour and brown sugar and cook until the pork is completely cooked through and the sauce has reduced and thickened slightly, 10 to 15 minutes. Season the filling with salt and pepper.
Lay one sheet of phyllo on a work surface. Using a pastry brush, spread melted butter evenly over the sheet. Top with another phyllo sheet and brush melted butter over the surface; repeat with 2 more layers of phyllo. Cut the phyllo stack into 12 even squares. Repeat this process with the remaining 4 phyllo sheets so there are a total of 24 cut squares.
Divide the shredded cabbage among the 24 phyllo squares, mounding it in the center of each square. Top the cabbage with about 1 tablespoon of the pork mixture, dividing it evenly among the squares. Brush the outer edges of each square with a little butter. Working one square at a time, bring the corners of the phyllo up and over the filling, twisting gently to create a purse. Transfer to a baking sheet and brush the outsides with a little melted butter.
Bake until the dough is crisp and golden brown, about 15 minutes. Serve immediately while still warm.