Step 1In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl using a hand mixer, cream together the butter and sugar until light and fluffy, 3 to 5 minutes. Add the vanilla and salt, and beat until fully combined. Slowly add the flour while beating, until all of the flour is fully incorporated, careful not to overbeat (overbeating will toughen the cookies).
Step 2Stir in the almonds, cashews and cherries by hand, making sure the nuts and fruit are evenly distributed throughout the dough.
Step 3Divide the dough in half and roll each half into a log about 2 inches in diameter. Press firmly to make sure the dough is holding together with the fruit and nuts. Wrap tightly in plastic wrap and refrigerate overnight.
Step 4Heat the oven to 375 degrees. Line 2 cookie sheets with parchment paper. Cut the logs into slices approximately one-fourth inch thick. Bake until the edges are golden brown, about 10 minutes. Cool the cookies on a rack.