Freeze the shortbread dough, and then grate it in a food processor to get the most tender crust.
Bring cranberries, water, and 1/4 cup of the sugar to a boil in a small saucepan over medium-high. Cook, stirring and smashing berries occasionally, until mixture thickens, 10 to 12 minutes. Remove from heat, and cool completely.
Beat butter, salt, and remaining 3/4 cup sugar in a large bowl with an electric mixer on medium speed until light and fluffy, 3 to 5 minutes. Add egg yolks and vanilla; beat on low speed until combined. Add flour to butter mixture; beat on low speed until combined.
Turn dough out onto a lightly floured work surface; knead until dough comes together, 3 to 4 times. Shape into a 14-inch-long log. Cover with plastic wrap, and freeze at least 1 hour or overnight.
Preheat oven to 350°F. Line a 9-inch square baking pan with parchment paper, allowing paper to extend past edges of pan. Grease paper.
Remove plastic wrap from dough log; cut in half crosswise, and cut each piece in half lengthwise. Feed dough log quarters through the chute of a food processor fitted with a shredding blade. Press half of grated dough into the bottom of prepared pan. Spread cranberry mixture over dough, leaving a 1/2-inch border. Top with remaining half of grated dough, pressing to seal edges.
Bake in preheated oven until firm and golden brown, 33 to 35 minutes. Cool in pan. Lift cranberry shortbread from pan using parchment as handles; cut into rectangles; then cut into triangles.