Core the pears from the bottom, keeping the stems in place and leaving walls about 1/2-inch thick.
Reserve the cores.
Place the pears upright in a large saucepan with the water, sugar, cinnamon stick, ginger and 1/2 cup Grand Marnier.
Cook the pears until they are tender but not mushy €” anywhere from 3-15 minutes, depending on the variety and ripeness.
Cool, then add another 1/4 cup Grand Marnier to the poaching liquid.
Let stand in refrigerator overnight.
Just before serving, whip together 1/2 cup heavy cream, the confectioners sugar and 1 tbs Grand Marnier in an electric mixer until stiff.
On slow speed, beat in 1/2 cup yogurt.
Remove pears from liquid; fill the cavities of the pears with this semistiff mixture.
Trim a 1/2-inch thick piece from each reserved pear core and plug the pear cavities to keep the filling in place.
To make the pears easy to eat, slice them horizontally at the point where the base narrows into the neck.
Melt the carob chips in a double boiler.
Slowly add 1/4 cup heavy cream and 1/2 cup yogurt, beating until smooth.
Heat just until warmed through; do not allow to simmer.