In a food processor, pulse the pine nuts and 1 cup of the flour until finely ground. Add the remaining flour and the salt and pulse to blend. With a hand mixer or a stand mixer fitted with the paddle attachment, beat the butter and granulated sugar on medium speed until light and fluffy, about 2 minutes. Add the vanilla and mix on medium until combined, about 15 seconds. Reduce the speed to low and gradually add the dry ingredients, mixing until the dough is just combined. Cover with plastic and refrigerate until firm, about 1 hour.
Position racks in the upper and lower thirds of the oven and heat the oven to 350°F. Line two cookie sheets with parchment or nonstick baking liners.
Using your palms, roll heaping tablespoonfuls of the dough into 1-1/2-inch balls. Arrange them 1 inch apart on the lined sheets. Bake until golden around the edges and light golden on top, 19 to 21 minutes, rotating and swapping the sheets halfway through for even baking. Transfer the cookies, still on their parchment, to a rack and let cool for 5 to 10 minutes, or until they have firmed up a bit and are cool enough to handle.
Put the confectioners' sugar in a small bowl. Gently toss the cookies in the sugar to coat; let them cool completely on racks. Toss them again in the sugar. The cookies will keep in an airtight container at room temperature for up to 1 week.