Preheat the oven to 375°F (190°C). Line two baking sheets with parchment paper.
Place butter in a small saucepan and cook over medium heat, stirring occasionally until the butter gets a nutty, brown color. It may take a few minutes.
Sieve the butter into a large bowl and let cool to room temperature.
Add both sugars over the brown butter and start mixing until creamy. Add egg and vanilla and continue mixing until well incorporated and creamy.
In a medium bowl mix flour with cream of tartar, baking soda, salt and cinnamon.
With the mixer on low gradually incorporate it into the butter mixture.
In a small bowl whisk together the sugar and cinnamon.
Use an ice cream scoop to take equal amounts of dough (about one big tablespoon) and roll it into balls with your hands.
Roll each ball into the sugar-cinnamon mixture and place it on the prepared baking sheet.
Sprinkle flaky sea salt (fleur de sel) on top of each.
Bake for 7-9 minutes until edges are browned and centers are puffed.
Cool completely on a cooling rack.