Preheat oven to 325F. Line a 9-inch round tart pan with removable bottom or an 8-inch square pan with parchment paper, leaving an overhang for easy removal.

In a large bowl with a hand mixer or in a stand mixer fitted with the paddle attachment, beat butter and granulated sugar on medium speed until light and fluffy, about 3 minutes. Scrape down the bowl and beat in vanilla extract.

Add flour and salt to the bowl. Mix on low speed just until a crumbly dough forms with no dry patches remaining, about 1 minute. Do not overmix.

Add chopped cranberries and pistachios. Mix on low speed or fold in by hand until evenly distributed throughout the dough.

Transfer dough to prepared pan. Press firmly and evenly into the bottom with your fingers or the bottom of a measuring cup to create a smooth, compact layer about 1/2 inch thick. Sprinkle coarse sugar and a few extra chopped pistachios on top, pressing gently to adhere.

Use a sharp knife to score the dough into 24 wedges (if round) or 24 squares (if square). Prick all over with a fork. Chill in the refrigerator for 15 minutes while oven finishes preheating.

Bake until the edges are firm and lightly golden and the center looks set but not browned, 22 to 26 minutes. The shortbread should still be pale overall.

Remove from oven and immediately re-cut along the scored lines using a sharp knife. Let cool in the pan for 10 minutes, then use the parchment overhang to lift out onto a cutting board. Transfer to a wire rack to cool completely. The shortbread will crisp as it cools.