1 cup (227 grams) unsalted butter, softened½ cup (100 grams) plus 2½ tablespoons (30 grams) granulated sugar, divided½ teaspoon (2 grams) vanilla extract2 cups (250 grams) all-purpose flour*½ cup (80 grams) white rice flour*1 teaspoon (3 grams) kosher salt
Spray a 9-inch square baking pan with baking spray with flour. Line pan with parchment paper, letting excess extend over sides of pan.
In the bowl of a stand mixer fitted with the paddle attachment, beat butter and ½ cup (100 grams) sugar at medium speed until light and creamy, 4 to 5 minutes, stopping to scrape paddle and bottom and sides of bowl. Beat in vanilla.
In a medium bowl, whisk together flours and salt. With mixer on low speed, gradually add flour mixture to butter mixture, beating just until combined and stopping to scrape paddle and bottom and sides of bowl. Spread dough into prepared pan, pressing even with your hands. (For completely smooth dough, top dough with a piece of parchment paper, and rub your hands on paper to smooth. Remove parchment.) Using a sharp paring knife or bench scraper, gently score top of dough into 24 (3×1⅛-inch) pieces. (See Note.) Dock each piece 2 to 4 times with a fork. Freeze until firm, about 15 minutes.
Preheat oven to 325°F (170°C).
Bake until top is dry and edges are lightly browned, 25 to 30 minutes. Sprinkle remaining 2½ tablespoons (30 grams) sugar onto hot shortbread, carefully tilting pan to evenly distribute sugar. Let cool for 5 minutes. Using a sharp paring knife or bench scraper, fully cut shortbread into pieces following scored lines. Let cool completely in pan on a wire rack. Using excess parchment as handles, remove from pan. Store in an airtight container for up to 1 week.