With a mixer, cream cookie butter, egg, vanilla extract, and brown sugar for about 4 minutes.
Add in flour, sea salt, baking soda, cinnamon, and nutmeg and mix until just combined. Dough should come together easily but not be crumbly. Do not over mix.
Divide dough into about 10 two-inch balls and place on a cookie sheet, spaced at least two inches apart. Cover pan tightly with plastic wrap and place in freezer for at least three hours (overnight is fine).
Preheat oven to 350 degrees. Remove plastic wrap then transfer pan directly from freezer to oven. Bake for about 12 minutes. Cookies should expand to about 3 inches in diameter with slightly domed centers and some crinkling on top.
Remove pan from oven and allow cookies to cool on pan. Cookies will be very soft to the touch at first but will get firmer as they cool.
To make ice cream sandwiches: Wrap cooled cookies tightly in plastic wrap and place in freezer until firm (at least 30 minutes but overnight is fine).
Remove cookies from freezer. Divide them up into pairs where each cookies is roughly equal in size.
Scoop one scoop of ice cream (slightly softened ice cream works best) onto flat (bottom) side of a cookie then press the flat side of another cookie down on top to make a sandwich. Repeat with remaining cookies.
If you want to take these cookie butter cookie ice cream sandwiches over the top, spread a bit of cookie butter on each cookie before adding the ice cream.