1. Pour the cream into a saucepan and add the honey. Place the saucepan over medium-high heat and bring to a boil. Lower the heat to medium-low to low and stir with a wooden spoon for about 3 minutes. Keep stirring to ensure the honey is dissolved and the cream does not burn. Turn off the heat, set it aside and allow to cool for about 5 minutes.
2. Place the honeydew pieces into a food processor or blender. Blend it until it turns to a puree. Add the honey cream mixture and blend until incorporated, about another minute.
3. Pour the puree into ice pop molds and freeze for at least 6 hours.
Serve immediately from the freezer or on ice with melon balls and mint for garnish.