Cream butter, granulated sugar, and ¼ cup (50g) brown sugar in a large bowl or the bowl of a stand mixer fitted with the paddle attachment.

Mix in egg and vanilla and salt, then slowly mix in flour until dough comes together.

Mix together remaining ¼ cup brown sugar and ground cinnamon in a small bowl.

Divide the dough in half. Place a large sheet of waxed paper or parchment paper on your work surface. Place half of the dough on the paper and press lightly to flatten; top with a second sheet of paper. Press and roll into an 8-inch square.

Sprinkle half the filling mixture over the dough, then tightly roll up the dough. Cover with plastic wrap and refrigerate until firm, at least one hour.

Repeat with second half of dough.

Preheat oven to 375°F. Line 2 cookie sheets with silicone baking mats or parchment paper.

Slice the cookie dough logs into ¼ to ½ inch thick cookies and place evenly spaced on cookie sheet (2-inches apart). Bake 8-10 minutes or unitl no longer glossy and the bottoms just start to turn golden brown. Cool completely before frosting.

Whisk together powdered sugar, vanilla, and milk (starting with 2 tablespoons and increasing a little bit at a time until you get a drizzle consistency). Drizzle over cookies.