Preheat oven to 275°. In a stand mixer, beat room temperature butter, 1/2 cup granulated sugar, the brown sugar, cinnamon, ginger, cardamom, nutmeg, and cloves on medium speed with paddle attachment until well blended and fluffy. Add rice flour and beat on low speed until incorporated, scraping bowl as needed. Gradually add all-purpose flour; beat on low until blended, scraping bowl occasionally.
Brush a 9-in. square nonstick snowflake shortbread pan with melted butter. Press 1 1/4 cups dough into pan until very even and smooth. Bake until shortbread is golden in center, 50 minutes. Reduce oven to 250°, drape shortbread with parchment paper, and continue to bake until a finger pressed lightly into center of dough leaves no imprint, 15 minutes more.
Set shortbread on a cooling rack and let cool 10 minutes. Loosen from pan with a thin sharp knife and invert onto a board. Sprinkle with 1 tbsp. granulated sugar and repeat to use remaining dough (for 5 batches total). After shortbread cools, if you find that you'd like it crunchier, set on a rimmed baking sheet, cover with parchment paper, and pop into a 250° oven for about 20 minutes.
Make ahead: Airtight at room temperature, up to 1 week, or frozen, up to 3 months.
Note: Nutritional analysis is per cookie.