Preheat the oven to 350°F. Line two baking sheets with parchment.  , To make the dough: In the bowl of a stand mixer fitted with the flat beater attachment or working in a large mixing bowl with an electric hand mixer, beat the butter, sugar, salt, and lemon zest or emulsion until smooth, 2 to 3 minutes at medium speed.  , Scrape the bowl, then beat in the egg and vanilla. , Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess.  , Add the flour and baking powder and mix until thoroughly incorporated. Scrape the bowl and mix again briefly. , Add the fruit and mix on low speed just until the fruit is evenly distributed and just beginning to break down. Be careful not to overmix or the dough will become pastel-colored instead of tie-dyed with streaks of bright fruit color. , To add the topping: Place the 1/3 cup (66g) granulated sugar in a small bowl. , Scoop approximately 2 tablespoons (about 38g) of dough (a level jumbo cookie scoop works well here) and roll in the sugar to coat. If the dough starts to feel soft and greasy, scoop the dough onto a baking sheet and chill in the refrigerator for about 10 to 15 minutes before rolling in sugar to allow the dough to firm up. , Arrange the sugar-coated balls of cookie dough on a baking sheet, leaving about 2" between them. , Bake the fruit cookies for 15 to 20 minutes, until the middles are set and the edges are browned. , Remove the cookies from the oven and let them cool right on the pan; serve warm or at room temperature. , Storage information: Store leftover fruit cookies, covered, at room temperature for up to 3 days; freeze for longer storage.