Filling: Stir together the sugar and cinnamon; set aside.
Cookies: Cream the butter and brown sugar until well blended with an electric mixer on medium speed.
Add the eggs and vanilla; blend well.
Combine the flour, baking powder, salt, and cinnamon; add to butter mixture and blend well.
Turn dough out onto a sheet of waxed paper; spread into a 9x6-inch rectangle using a rubber spatula.
Sprinkle the cinnamon-sugar to within 1 inch from the edges.
Roll dough up jelly-roll style.
Roll in remaining cinnamon-sugar; wrap dough tightly in plastic wrap.
Refrigerate for 2 - 4 hours.
Preheat oven to 350°F.
Slice dough 1/4-inch thick; place 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.