Cook the peaches: In a medium skillet, combine the 3 cups peach chunks, the brown sugar, and butter over medium heat. Cook, stirring occasionally, for about 10 minutes, or until the peaches have softened and the mixture is thick and saucy, almost like a chunky jam. As the peaches cook and soften, gently mash some of them with the back of a spoon. Set aside to cool completely.

Make the ice cream: In a large bowl using a hand mixer or stand mixer fitted with a whisk attachment, whip the cold heavy cream until stiff peaks form, about 4 minutes. Transfer the whipped cream to another bowl and place in the refrigerator.

Place the cream cheese in the mixing bowl you just used and beat on medium-high speed until smooth (no lumps). Add the sweetened condensed milk, vanilla extract, and cinnamon, then beat until combined. Add the whipped cream back into the bowl with the cream cheese mixture, and beat on low speed until just combined.

Spoon/spread about a third of the ice cream mixture into a deep freezer-safe container or bowl. I suggest a 9×5-inch loaf pan. Drop spoonfuls of about half of the cooled peaches on top. Sprinkle half of the Biscoff pieces over the top. Spoon/spread another third of the ice cream mixture on top, followed by remaining peaches and Biscoff pieces. (If desired, reserve a few of the peaches and Biscoff crumbs for the top.) Top with the remaining ice cream mixture (and any reserved peaches and Biscoff). With a knife, gently swirl the peaches, Biscoff, and ice cream together. Cover tightly and freeze for at least 8 hours and up to 2 weeks.

Scoop, serve, and enjoy!