Gently peel the pears, then use a melon baller or small paring knife to carefully remove their cores from the bottom, keeping the pears whole.
In a medium saucepan over medium heat, combine the 2 cups of granulated sugar, cinnamon sticks, star anise, and 2 cups of water (or wine). Stir occasionally until the sugar fully dissolves and the mixture comes to a boil.
Carefully place the prepared pears into the hot syrup. Reduce the heat to medium-low, cover the saucepan, and let the pears gently simmer for about 8 minutes. They should be tender when gently poked with a knife.
Remove the saucepan from the heat and allow the pears to cool slightly in the syrup while you prepare your delicious chocolate sauce.
In a separate small saucepan over medium heat, whisk together the cocoa powder, the remaining ½ cup granulated sugar, and 1 cup of water. Bring this mixture to a gentle boil, making sure to whisk continuously.
Take the chocolate sauce off the heat. Immediately whisk in the cut butter and finely chopped semi-sweet chocolate until the sauce becomes wonderfully smooth and glossy.
Carefully lift the poached pears from the syrup and place them onto serving plates. Drizzle generously with the warm chocolate sauce and serve right away for a delightful, comforting treat!