Add the strawberries to a blender and blend until smooth. (Pour through a sieve if desired; discard solids.) Pour purée into a medium saucepan. Bring mixture to a bubbling simmer, stirring occasionally, and let cook until thickened and coats the back of a spoon or spatula, 20 to 30 minutes. (Mixture will continue to thicken as it cools.) Transfer to the refrigerator; cool completely before using.

In a large bowl, stir together sweetened condensed milk and strawberry mixture. In another bowl or the bowl of a stand mixer, whip heavy cream on high speed until stiff peaks just begin to form.

Add half of strawberry mixture to whipped cream. Mix on low speed until mostly combined. Repeat with second half of strawberry mixture. Whip on high speed until stiff peaks form again.

Using a sharp knife or apple/potato peeler, shave chocolate into small pieces or “flecks”. Fold into strawberry mixture.

Spoon mixture into a loaf pan and freeze for 4 to 6 hours, or overnight. Thaw slightly before serving.