Peel the pears and cut them in half from top to bottom, leaving the stems intact. Core each pear half by scooping out the center with a melon baller or spoon.
Add the water, honey, and sugar to a 4-quart pot and bring to a boil over high heat. Stir until the sugar and honey are dissolved, then add the ginger, cloves, star anise, and cinnamon stick.
Slip the pears into the liquid and turn the heat down to a simmer. Cover and cook for 20 to 30 minutes, or until the pears can be just pierced with a fork.
Transfer the pears and the poaching liquid to a smaller container, cover, and refrigerate overnight. (You can eat the pears immediately, if you want, but they will have a deeper flavor after steeping overnight in the poaching liquid.) The next day drain and serve the pears.
If you wish you can reduce the poaching liquid into a syrup; place in a wide saucepan and simmer for 30 minutes or until syrupy and reduced by half.