Pulverize the strawberries in a food processor or blender until smooth.
24 oz strawberries
Add the puree and sugar to a saucepan over medium low and simmer (stirring every few minutes, scraping the sides) until the strawberries reduce by half and the mixture falls slowly from a spatula or spoon and turns much thicker. About 20-30 minutes.
½ cup granulated sugar
Transfer to a bowl, place in the fridge, and cool to at least room temperature, stirring every few minutes to release heat and steam.
Place the stand mixer bowl and whisk attachment in the freezer for 15 minutes. Then, whip the heavy cream on high speed until stiff peaks form.
2¼ cups heavy whipping cream
In a large bowl, combine the sweetened condensed milk, vanilla, and ¾ cup of the strawberry sauce and mix until incorporated.
1 can sweetened condensed milk, 1 tablespoon vanilla paste or extract
Optional: Add a few drops of red food coloring to brighten up the final product. Adding the whipped cream will lighten the color significantly.
In two batches, fold in the whipped cream until completely combined and no white streaks remain. Do this carefully so the mixture doesn't become deflated.
Add half of the ice cream to a standard loaf pan, drizzle half of the remaining strawberry sauce over the top, and swirl it in with a butter knife. Scatter on half of the chunks of cheesecake if using.
1 slice cheesecake
Add almost all of the remaining ice cream, then add more cheesecake pieces, pressing them down slightly. Add the remaining ice cream and smooth it out on top, then drizzle on the remaining strawberry puree and swirl it in.
Cover tightly with plastic wrap and foil and freeze for at least 6 hours.