Whisk all ingredients except gingersnaps and bourbon in a bowl to blend. Strain into an ice cream maker and freeze according to manufacturer's directions.
Scrape ice cream into a bowl and stir in gingersnaps and bourbon. Freeze, covered, until scoopable, 2 1/2 hours and up to 1 week (gingersnaps soften somewhat after 1 day).
Note: Nutritional analysis is per 1/2-cup serving.