In an electric mixer fitted with the paddle attachment, beat the butter at medium speed for about 1 minute. Gradually add the confectioners' sugar and increase the speed to medium-high. Occasionally stopping to scrape down the sides with a rubber spatula, continue to beat until it is pale and fluffy, an additional 4 to 5 minutes. Add the vanilla extract and orange zest.
Sift together the flour, spices and salt, then blend with the almond meal. Add this to the creamed butter all at once, then stir with a wooden spoon or spatula for a couple of turns. Return the bowl to the stand and mix on the lowest speed until the flour is just incorporated without over-mixing. Turn out the dough onto a large piece of plastic wrap, push together to form a large flat disc, and wrap well. Refrigerate until very firm, at least 2 hours or overnight.
Preheat the oven to 375 degrees F. Line a large baking sheet with parchment paper or nonstick liner.
Scoop out the dough in tablespoons, roll into a ball and place on the cookie sheets, about 2 inches apart. Using a small spoon dipped in flour, press down on each ball so it forms a round disc about 1/2-inch thick. The dough will be fragile but if it cracks or the dough falls apart it can be gently pressed together or reshaped. Repeat with remaining dough.
Bake the cookies until the edges are lightly golden, though the tops will still be pale, 14 to 18 minutes. Remove from the oven and while still warm, sprinkle generously with confectioners' sugar. Using a spatula, carefully remove the cookies and lay out on a cooling rack.