Filling: Stir together the 1/4 cup of sugar and the 1 Tablespoon of cinnamon; set aside.
Cookies: Cream the butter and sugar until well blended with an electric mixer on medium speed.
Add the egg and vanilla; blend well.
Combine the flour, baking powder, and salt; add to butter mixture and blend well.
Turn dough out onto a sheet of waxed paper; spread into a 9×6-inch rectangle using a rubber spatula.
Sprinkle the cinnamon-sugar filling to within 1 inch from the edges.
Roll the dough up jelly-roll style.
Roll in any remaining cinnamon-sugar that spilled out; wrap dough tightly in plastic wrap.
Refrigerate for 2-4 hours.
Preheat oven to 350°F.
Slice dough into 1/4-inch thick slices; place them 2 inches apart onto parchment-lined cookie sheets.
Bake for 8 minutes or until golden on top (take them out before they look done and allow to firm up on the cookie sheet).
Cool for 4 minutes on the cookie sheets, then remove to racks and cool completely.
Once cookies have cooled, make the glaze by using an electric mixer to mix the butter, powdered sugar and vanilla. Add hot water, 1 tablespoon at a time, until the glaze has reached desired consistency.
Place glaze in a ziploc bag, cut a small hole in the corner, and pipe glaze onto cookies, following the swirl of the cookie. Allow to set.
