To toast the coconut, preheat oven to 325°F. Spread flaked coconut into a thin layer on a large, rimmed baking sheet. Bake for 5 minutes, stir, and then bake for 1 to 3 more minutes or until light golden brown. Set aside to cool completely.
In a large bowl, use an electric mixer to beat the butter until creamy. Mix in the powdered sugar, salt, vanilla extract, and almond extract and beat for 1 minute until light and smooth. With mixer on low speed, slowly add the flour, blending until just incorporated. Add the toasted (cooled) coconut and quickly mix it in until thoroughly combined.
Turn the dough out onto a work surface and shape it into a rough ball. Cut the ball in half and form each piece of dough into an 8-inch log. Tightly wrap each log in plastic wrap and freeze for 30 to 40 minutes.
Preheat the oven to 325°F. Line two baking sheets with parchment paper. Remove one log of dough from the freezer. Cut the dough into 1/4-inch thick slices, rolling the log every few slices to maintain the round shape of the cookies. Arrange the cookies on the prepared baking sheet. Bake until the cookies start to turn a light golden color around the edges, between 14 and 16 minutes. Allow to cool on baking sheets.
Repeat the steps with the second log of cookie dough. Once the cookies are completely cool, store them in an airtight container.