Make the cherry jam by combining cherries and honey in a small pot over medium high heat. Cook until cherries break down slightly and thicken, about 10 minutes. Allow to cool completely.
In a large bowl, use a hand mixer or stand mixer to whip the cream to stiff peaks.
In a second large bowl add sweetened condensed milk and using a spatula stir for about 1 minute until is loosens. Add 1/2 of the cherry jam and stir to combine.
Fold in 1/3 of the cream to the cherry milk mixture. Add in the remaining cream and gently fold to preserve as much air as possible.
In your 9x13 pan, layer 1/2 of the cherry ice cream base, a few tablespoons of the cherry jam and 1/4 cup of chocolate cookie crumbs.
Repeat the layering process. Freeze for 4-6 hours or over night.