In a small saucepan, place 1/2 cup of the honey and 1/2 cup water and heat over medium heat. Bring to a boil. Reduce the heat and simmer for one minute. Remove from the heat and let cool completely.
In the work bowl of a food processor, pulse the pears and lemon juice until finely chopped. Add the cooled honey mixture and process until smooth. Chill until very cold, at least four hours.
Meanwhile, make the sauce. In a small saucepan, place the port, vinegar, remaining two tablespoons honey, the cinnamon stick, and the star anise. Bring to a boil. Reduce the heat to low and simmer until the syrup has thickened and reduced to about 1/3 cup, about 30 minutes. Watch the pan carefully during the last five to 10 minutes of cooking; it can very quickly go from perfect to burned and bitter. Remove from the heat and let cool to room temperature before serving; remove and discard the cinnamon stick and star anise.
When the pear puree is cold, freeze it in an ice cream maker according to the manufacturer’s directions. The sorbet is best served at once, but it may be transferred to a freezer-safe container and frozen until ready to serve. Let stand at room temperature for 15 minutes before serving.
If not using an ice cream maker, transfer the cold pear puree to a shallow glass or stainless-steel dish. Cover and place in the freezer until frozen solid, about 6 hours. Let the frozen mixture stand at room temperature for 10 minutes. With a large metal spoon, break the puree up into smaller pieces. Transfer the mixture to the work bowl of a food processor. Process until smooth and creamy, occasionally scraping down the sides of the bowl. Serve immediately or place back into the freezer for up to 1 hour before serving. The sorbet will freeze solid but it can simply be processed again until creamy just before serving.
To serve, scoop the sorbet into individual serving bowls and drizzle the syrup over each. Garnish with pear slices if desired.
The sauce can be made ahead of time. Just transfer it to a glass measuring cup and let stand at room temperature for several hours, or for longer storage, cover and refrigerate. Before serving, heat in a microwave oven on high power for a few seconds, just until liquid and pourable.