Preheat the oven to 350 degrees F. and adjust the oven rack to middle. Line a sheet tray with parchment.
Melt the butter to a large skillet over medium heat. Cook until the butter is golden brown. Remove the butter to a large bowl to cool.
Once cool, add the brown sugar and stir until smooth. Stir in the egg and vanilla, mixing until well combined.
In another medium bowl, whisk together the flour, cinnamon, ground ginger, baking soda, baking powder, and salt. Add the dry mixture to the butter mixture and stir until well incorporated and smooth, about 1 minute.
Add the granulated sugar to a plate. Divide the dough into 12 equal-sized balls and roll them in the sugar. Arrange the dough on the parchment paper lined sheet tray at least 2 inches apart. Bake for 10 to 12 minutes.
Cool the cookies on the sheet tray for 5 minutes, then transfer to a cooling rack for another 10 minutes.
Turn 6 cookies face up on the counter. Scoop 1/2 cup of ice cream on cookies and using an offset spatula, spread evenly to the edges. Top the ice cream with a second cookie and press down to adhere. Freeze until solid, about 2 hours.