Pour the chopped walnuts into a nonstick skillet. Toast the nuts over medium heat, stirring them often, for several minutes until the walnuts are fragrant and toasted. Remove the nuts from the heat and let them cool.
Make the batter
Preheat the oven to 350° F. Line a large baking sheet with parchment paper.
Cream together the butter and sugar in the bowl of a stand mixer or with a hand mixer, for 5 minutes. The mixture should be light and fluffy.
Blend in the eggs one at a time, followed by the vanilla and the rum extracts.
Whisk together the flour, salt, baking powder, and baking soda in a separate bowl. Stir the walnuts and the coconut into the flour mixture.
Add the dry mixture to the butter-sugar mixture in two or three additions, alternating with the sour cream. Do not overmix: pulse the mixer as you add in the ingredients, and finish the mixing with a wooden spoon.
Get ready to bake
Scoop the batter in 2-teaspoon sized scoops and place them on the prepared baking sheet, about two inches apart.
Bake the cookies for 15-17 minutes, until they're puffed and lightly browned around the edges. Move the cookies to a cooling rack.
Store the cookies in a sealed container for up to one week. Makes about 36 cookies.