In a medium saucepan, bring the milk and honey to a simmer over moderate heat, stirring to dissolve the honey, about 4 minutes. Remove from the heat and stir in the ground almonds and the almond extract. Strain the almond milk through a sieve into a heatproof bowl set in an ice water bath and let cool completely. Transfer the almond milk to an ice cream maker and freeze according to the manufacturer's instructions.
The ice milk can be frozen in an airtight container for up to 1 week.