Toast 1 cup of coconut in a medium skillet over low heat. Stir almost constantly until the coconut begins to brown. Remove from heat to a plate or bowl and let cool.
Whisk pudding and milk in a medium bowl for about 2 minutes. (There may still be some lumps from the coconut in the mix.) Set aside to firm up.
Make the crust: place the shortbread cookies in a large gallon size resealable bag. Seal the bag except for 1” (to allow air to escape) and roll the bag with a rolling pin to crush the cookies. There is no need to get them to a super fine crumb, some chunks may remain. Reserve 1/4 cup of the crumbs for garnish, then pour the melted butter into the bag, squeezing it to work it through the crumbs. Press the crust into a 9x9 pan.
Place cream cheese in a large bowl. Beat it with a hand mixer for 1 minute, until it’s smooth. Add the set pudding and mix until mostly no lumps remain.
Stir the coconut extract, if using, into the tub of Cool Whip. Mix half the tub of Cool Whip into the pudding mixture, along with 2 cups of coconut. Spread over crust. Top with remaining whipped topping and sprinkle with reserved crushed cookies and toasted coconut.
Cover and chill for at least 4 hours before serving. This will last in the refrigerator for up to 3 days.