04Gradually whisk the hot mixture into the cream cheese until smooth. Pour into a thick plastic resealable 1-gallon bag; submerge the bag in the ice bath. Let stand, adding more ice to bath as necessary, until mixture is cold, about 30 minutes. Place in an ice cream maker and churn until thick and creamy.05Meanwhile, make the swirl, if using: In a saucepan, bring the berries and sugar to a boil over medium-high heat. Boil, stirring occasionally, until the temperature reaches 220 degrees, about 5 to 8 minutes. Let cool slightly, then strain through a sieve into a bowl, pressing on the berries to release their juices. Cool in an ice bath as in Step 4, or refrigerate until cold.06Pack the ice cream into a quart storage container in about four layers, alternating with layers of fruit swirl, and ending with a spoonful of swirl. Do not mix. Press parchment or plastic wrap against the surface, and seal with an airtight lid. Freeze until firm, at least 4 hours. Serve with sugared berries if the ice cream was made without the swirl.