For Ice Cream: Combine first 4 ingredients in bowl. Combine milk and cream in medium saucepan. Add dry ingredients; whisk until well blended. Cook and stir on medium heat until mixture reaches 165°F.
Pour small amounts of mixture into blender and process 30 seconds. Transfer to clean bowl and chill over an ice bath. Continue until all of mixture has been processed. Refrigerate overnight.
Freeze mixture in ice cream maker according to manufacturer's directions. Spoon prepared ice cream into freezer container. Gently fold in OREO Pieces. Freeze until very firm.
For Each Serving: Use #30 scoop to portion 2 scoops (1.35 oz.) ice cream into martini glass. Pour espresso and liqueur over ice cream just before serving. (Keep remaining ice cream frozen to use for other servings.)