Preheat your oven to 350°F (175°C). In a mixing bowl, whisk together the all-purpose flour, bread flour, baking soda, and salt until well combined.

In another bowl, beat together the softened butter, sugar, and brown sugar until light and fluffy. Add the eggs and vanilla extract, mixing until fully combined.

Gradually add the flour mixture to the buttery mixture, mixing until just incorporated. Use a cookie scoop to place tablespoon-sized balls of dough onto baking sheets lined with parchment paper.

Bake the cookies for 8-10 minutes until the edges are golden brown but the center remains soft. Sprinkle coarse salt on each warm cookie and let them cool on a wire rack.

Whip the heavy cream in a large bowl until stiff peaks form. Fold in the sweetened condensed milk, vanilla extract, and a touch of salt until fully combined.

Melt the butterscotch chips and let cool slightly. Fold the cooled butterscotch into the whipped cream mixture until fully combined. Transfer to lined cake pans and freeze for about 2 hours or until solid.

Once the ice cream is set, slice it using a round cutter. Take two cookies and place a round of butterscotch ice cream between them. Wrap each sandwich in plastic wrap and return to the freezer to set further.