First begin make the blue cheese ice cream. Mix together the egg yolk, milk, cream, and sugar in a medium-sized saucepan over low heat.
Once the mixture is warm, but not hot, add the blue cheese and stir until blended.
Continue to cook over low heat until the mixture is hot but not boiling, stirring every minute or two. Remove it from the heat and then refrigerate for at least 4 hours, or overnight.
While the blue cheese ice cream base is cooling, make the blackberry honey swirl.
Mix together all of the ingredients except the cinnamon in a small saucepan over medium-high heat.
Allow the mixture to come to a boil, then lower the heat and simmer the mixture for 20 minutes, stirring every few minutes.
Then remove the pan from the heat, stir in the cinnamon, and refrigerate until use.
Once the ice cream base has adequately chilled, remove it from the refrigerator and prepare it according to the directions on your ice cream maker.
During the last few minutes of churning, pour in the blackberry honey sauce.
Once the ice cream has been adequately churned, place it in a freezer-safe container and store it in the freezer for 4 hours before serving.
