Make the cookies: Whisk the flour, baking powder, baking soda and salt in a medium bowl. Beat the butter and brown sugar in a large bowl with a mixer on medium-high speed until fluffy, 3 to 4 minutes. Beat in the tahini. Beat in the eggs one at a time until combined, then beat in the vanilla. Reduce the mixer speed to low; beat in the flour mixture in two batches, alternating with the sour cream. Cover the dough with plastic wrap and refrigerate until firm, about 1 hour.
Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Scoop heaping tablespoon-size balls of dough and arrange about 1 1/2 inches apart on the prepared pans. Bake until the cookies are set around the edges but still soft in the centers, 12 to 14 minutes. Let cool 10 minutes on the pans, then transfer to racks to cool completely.
Make the glaze: Combine the confectioners' sugar, lemon zest, 3 tablespoons lemon juice and the salt in a medium bowl; whisk until smooth. (If the glaze is too stiff, add more lemon juice, 1 teaspoon at a time.) Drizzle on the cooled cookies. Let set about 10 minutes.