Position racks in the upper and lower thirds of the oven; preheat to 350˚. Spread the almonds on a baking sheet and bake on the lower rack until toasted and lightly browned on the inside, 15 to 18 minutes. Let cool completely, then pulse in a food processor until very finely ground (do not grind to a paste). Add the all-purpose flour, rice flour, 1 teaspoon cinnamon and the salt. Pulse until combined.
Line 2 baking sheets with parchment paper. Beat the butter and 1/2 cup confectioners' sugar in a large bowl with a mixer on medium-high speed until pale and fluffy, about 3 minutes. Beat in the vanilla until combined. Reduce the mixer speed to low and beat in the flour mixture. Turn out the dough onto a large sheet of plastic wrap, flatten into a rectangle and wrap. Refrigerate until firm, about 1 hour.
Roll out the dough between 2 sheets of plastic wrap into an 8-by-9-inch rectangle (about 1/3 inch thick). If the dough starts to crack around the edges, pinch it back together with your fingers. Peel off the plastic wrap. With a short side facing you, slice the dough lengthwise into eight 1-inch-wide strips, then slice the strips crosswise into 1 1/2-inch rectangles (48 total; if the dough becomes too soft, refrigerate 15 minutes). Arrange the rectangles 1 inch apart on the prepared pans.
Bake, switching the pans halfway through, until the cookies are set around the edges, 16 to 20 minutes. Let cool 5 minutes on the pans.
Meanwhile, whisk the remaining 1 cup confectioners’ sugar and 1 teaspoon cinnamon in a shallow bowl. Gently toss the warm cookies in the sugar mixture to coat, then transfer to racks to cool completely. Toss the cooled cookies in the sugar mixture again.