Add strawberries, jam, sugar, and lemon juice to a medium-sized pot and bring to a boil over medium-high heat, stirring occasionally.
Continue to boil for an additional 8-10 minutes until juices have released, strawberries have softened and the sauce has thickened quite a bit to concentrate the berries.
Remove strawberries from heat and allow them to cool. Then place them in the refrigerator for 1 hour to completely cool them down.
Whip heavy cream to stiff peaks and set aside.
Add cream cheese to the bowl of a stand mixer or a medium-sized bowl if using a hand mixer.
Beat on medium-high speed, then slowly add in condensed milk and vanilla extract, and mix until completely smooth.
Turn off the mixer and fold whipped cream into the cream cheese mixture using a spatula.
Once whipped cream is folded in, carefully fold in the strawberries into the batter, only folding 3-4 times just until the strawberries have distinctly swirled through the batter (don’t over fold the strawberries because you will turn the entire ice cream mixture pink).
To freeze, alternate adding ice cream mixture and crumbled cake to freezer-safe containers. Freeze for at least 5-7 hours then serve.
Let the ice cream sit out for 5 - 10 minutes before serving.