Mix the softened cream cheese and honey in a medium mixing bowl until well combined. Add in the milk, almond extract, fresh lemon zest, and salt, and combine. Finally, add the heavy cream and mix until well-combined.
Cover the bowl with plastic wrap and place in the refrigerator to chill for at least 2 hours (although you can chill it overnight).
Meanwhile, combine the fresh diced strawberries, honey, and pinch of salt in a small saucepan over medium heat. Stir frequently until the strawberry mixture begins to simmer. Use a fork or potato masher to mash the berries.
Continue to simmer for about 10 minutes, or until the strawberry sauce as slightly thickened and reduced in volume.
Transfer mixture to a glass container and store in the refrigerator until ready to freeze.
When chilled and ready to freeze, pour the cheesecake ice cream mixture into your chilled freezer-safe container.
Then spoon the strawberry sauce onto the cheesecake ice cream base in the shape of a cross (for a round dish) or in several parallel lines (for a bread pan).
Use a butter knife to make a circle, swirling the strawberry mixture into the ice cream mixture, cover, and place in the freezer.
Stir the ice mixture every 30-45 minutes, scooping the ice cream along the edge into the center to allow everything to freeze evenly.
Freeze for an additional 4-5 hours.