Digital kitchen scale, Measuring cups, Measuring spoons, Digital instant read thermometer, 11-inch tart pan with removable bottom, Half sheet pan, Parchment paper or silicone baking mat, Small skillet, Small bowl, Medium bowl, Whisk, Stand mixer with paddle attachment, Rubber spatula, Cake pan (optional), Wire cooling rack, Cutting board, Pastry brush, Thin spatula
Preheat the oven to 300 degrees F. Grease an 11-inch tart pan with a removable bottom. Line a rimmed baking sheet with parchment paper or a silicone baking mat.
In a medium bowl, whisk together the all-purpose and rice flours, 1/2 teaspoon of the salt, and 2 tablespoons of the dulse granules. Combine the remaining 1/2 teaspoon salt and 1/2 tablespoon dulse in a small bowl and reserve for sprinkling over the top of the shortbreads.
Beat the butter and sugar together in a stand mixer fitted with the paddle attachment on medium speed until creamy and lightened in color, 3 to 5 minutes, scraping down the sides of the bowl as needed. Turn off the mixer, add the flour mixture all at once, then return the mixer to its lowest speed until the flour is incorporated and the mixture is the texture of crumbly wet sand, about 30 seconds.
Transfer to the prepared tart pan and use your hands or the bottom of a cake pan to press the mixture into an even layer. Bake until the shortbread is set and the edges are golden brown, about 1 hour. Cool in the pan on a wire rack for 5 minutes. Leave the oven on.
Remove the outer ring of the tart pan, then carefully transfer the shortbread onto a cutting board, using a paring knife to separate the pan bottom if necessary. Brush the shortbread with the egg mixture, then evenly sprinkle all of the dulse-salt mixture over the top. Slice into 16 wedges and transfer to the parchment-lined baking sheet.
Return to the oven and bake until the egg wash is set, 8 to 10 minutes, then transfer the shortbreads back to the wire rack to cool completely before serving.