Whisk the flour, salt, baking powder and baking soda in a medium bowl. Beat the butter and granulated sugar in a large bowl with a mixer on medium-high speed until light and fluffy, 3 to 5 minutes. Beat in the egg, then the vanilla and lemon extracts. Reduce the mixer speed to low and beat in the flour mixture until just combined.
Remove half the dough to a large piece of plastic wrap, flatten into a disk and wrap. Add 2 tablespoons gelatin powder, the lemon zest and juice and the yellow gel food coloring to the remaining dough and beat until combined. Turn out onto another piece of plastic, flatten into a disk and wrap. Refrigerate both disks until firm, at least 2 hours or overnight.
Roll out each disk of dough into a 10-by-11-inch rectangle on a lightly floured surface. Put the plain dough on top of the lemon dough and trim the edges. Sprinkle 1 tablespoon yellow sanding sugar over the top of the dough and gently spread to evenly cover. Starting with a long end, roll up the dough into a log. Wrap in plastic wrap and refrigerate until firm, at least 3 hours or overnight.
Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Mix the remaining 2 tablespoons gelatin powder, 1 tablespoon yellow sanding sugar and the coarse white sugar in a bowl; sprinkle on a sheet of parchment. Roll the dough in the sugar mixture, pressing to adhere. Slice the log into 3/8-inch-thick rounds; arrange 1 1/2 inches apart on the prepared baking sheets. Bake, switching the pans halfway through, until the cookies are puffed and set around the edges, about 15 minutes. Let cool 5 minutes on the pans, then transfer to racks to cool completely.