Wash your cherries, remove the stem, and pit them using a cherry pitter. Slice your cherries in half. If you do not have a cherry pitter you can cut your cherries in half and pry the pit out with a spoon or knife (be careful!). Transfer your cherries to a large bowl.
Stir the sweetened condensed milk in with the cherries and set aside.
Pour the chilled whipping cream into the bowl of your stand mixer and using the whisk attachment whisk until stiff peaks form. This will take about 5 minutes. Half way through the mixing, add the honey or the sugar. Be careful not to over mix.
Add the whipped cream to the bowl with the cherries and sweetened condensed milk and fold everything together using a rubber spatula.
Gently fold in your chocolate chunks.
Pour into a loaf pan. We used a 5 X 11 inch loaf pan.
Cover with plastic wrap so that the plastic actually touches the surface of the ice cream mixture; this will eliminate ice crystals from forming on the top of your ice cream. As an extra precaution against ice crystals we also place the plastic covered loaf pan in an extra large freezer bag. Place your loaf pan in the freezer.
Freeze overnight.
Scoop and enjoy!