Black walnuts are known for their robust flavor, but regular walnuts also work well in these buttery, melt-in-your-mouth cookies.
Preheat oven to 350 degrees. Toast nuts on a rimmed baking sheet until fragrant and golden, about 10 minutes. Let cool.
Beat butter and granulated sugar with a mixer on medium speed until pale and fluffy, 3 to 4 minutes. Beat in orange zest. Reduce speed to low; add flour and salt, scraping down side of bowl as needed. Mix in walnuts.
Divide dough in half, and transfer each to an 8-inch square baking dish, pressing down until flat. Refrigerate for 15 minutes. Prick lines into dough every inch with a fork. Bake until pale golden, about 25 minutes. Remove from oven. Sprinkle Demerara sugar over surface of each. Bake until sugar is set, about 5 minutes. Let stand for 5 minutes. Cut into 2-inch squares while warm. Transfer pans to wire racks, and let cool.
Cookies can be stored in an airtight container at room temperature for up to 1 week.