Preheat oven to 350°F (175°C) and prepare an 8x8 inch baking pan with parchment paper.

In a mixing bowl, combine softened butter, granulated sugar, and light brown sugar; blend until smooth and creamy.

Add egg and vanilla extract to the mixture, mixing until well incorporated.

In a separate bowl, whisk together flour, cream of tartar, baking soda, salt, and cinnamon.

Gradually add dry ingredients to the wet mixture, folding gently until just combined.

Spread the cookie dough evenly in the lined baking pan, pressing it down firmly.

For the filling, mix melted butter, brown sugar, cinnamon, and flour in a small bowl until smooth; spread over cookie base and swirl with a knife.

Bake in the preheated oven for 20-30 minutes until edges are golden and a toothpick comes out clean.

Whisk together powdered sugar and heavy cream for icing; adjust thickness as desired.

Cool the bars for 10 minutes in the pan, then lift out using parchment and cool completely on a wire rack. Drizzle icing before serving.