Whip the cold heavy whipping cream on medium speed just until stiff peaks form; about 2-3 minutes. Set the bowl aside.
In a separate bowl, whisk together the sweetened condensed milk, lemon juice, lemon zest, and vanilla extract until combined.
Gently fold the whipped cream and lemon mixture together until totally combined. Fold in most of the shortbread or lemon cookie pieces, reserving some for the top.
Pour ice cream mixture into a standard size loaf or 9x9 pan and spread into an even layer.
Sprinkle on the rest of the shortbread cookie pieces on top of the ice cream.
Freeze for at least 6 hours, or overnight. Enjoy!
Notes
*Using 2 medium-sized lemons should give you roughly 2 tablespoons of zest and about ⅓ cup of lemon juice.