For the Butterscotch Sauce:
1/2 cup heavy cream
1/2 cup dark brown sugar, packed 110 grams
1/2 cup salted butter 113 grams or 8 tbsp
pinch of flaky sea salt

For the Cookies:
1 cup + 2 tbsp salted butter See note below if you want to skip the brown butter. You'll start with 254 grams and want 206 grams left after browning.
1/3 cup + 1 tbsp butterscotch chips, melted
3/4 cup dark brown sugar, packed 163 grams
3/4 cup granulated sugar 156 grams
2 large eggs, at room temperature
1 and 1/2 tsp vanilla extract
3 cups all-purpose flour, spooned & leveled 390 grams
1 tsp baking powder
1 tsp baking soda
1/2 tsp salt

For the Butterbeer Frosting:
6 tbsp salted butter Brown it if desired, or not if you want one fewer step
4 and 1/2 ounces cream cheese This only needs 5 mins or so at room temp
2 and 1/4 cups powdered sugar
3/4 tsp vanilla extract
1/3 cup butterscotch sauce
pinch of salt to taste