With a mixer on medium, cream the butter and sugar until they're fluffy, about 30 seconds. Add the vanilla extract (and almond extract, if you're using it) and mix for another 10 seconds until the extract is incorporated. Add the salt and flour. Set the mixer to low and blend for a few seconds, then increase the speed to medium and mix until the dough is well combined, about 30 seconds. Mix in fruit and nut mixture. Firm the dough in the freezer for 15 minutes.
Heat the oven to 350° and flour a work surface. Roll the dough into two logs about 1½ inches in diameter. Wrap them in plastic wrap and freeze them for 15 minutes.
Cut the logs into 1/4-inch slices and place them 2 inches apart on a baking sheet. Bake until the cookies are just beginning to turn golden on the edges, 10 to 12 minutes.