Prepare your ice cream machine according to manufacturer's directions.
Stir milk, cream, sugar, and honey into a saucepan over low heat until the sugar and honey are dissolved.
Remove from heat and put into a container. Mix in vanilla extract and chill until very cold (a minimum of 2 hours to overnight).
Pour cold ice cream mix into your ice cream maker and start churning to the manufacturer's directions.
Break up strawberry pocky sticks into small pieces.
Once the ice cream starts forming softly, put in the strawberry pocky pieces and continue to mix.
Once it's ready, serve or place in freezer for later (place plastic wrap directly on the ice cream if freezing).
Serve with honeycomb or a drizzle of honey and extra Pocky sticks!