In a medium bowl, whisk together the flour, cream of tartar, baking soda and Sel Gris. Set aside.
Cream together the butter and 1 1/2 cups of sugar until in the bowl of a stand mixer fitted with a paddle attachment until light and fluffy. Scraping down the sides as needed. Add the eggs, one at a time, beating well after each addition. Add the flour mixture, and continue beating until combined. Cover the mixing bowl with plastic wrap and refrigerate for at least two hours.
When ready to bake, preheat the oven to 350°F and line two baking sheets with parchment paper. In a small bowl, combine 1/4 cup sugar with the cinnamon.
Using a cookie scoop, scoop about two tablespoons of cookie dough and flatten it slightly. Place a caramel in the center of the dough and then cover the caramel completely with the dough. Roll the cookie into a ball then lightly roll it in the cinnamon-sugar mixture on all sides. Place the cookie on the baking sheet then repeat the filling process with the remaining dough, spacing the cookies at least 2 inches apart. Sprinkle the tops of each cookie with a small pinch of Inspiced sea salt.
Bake the cookies for 12 to 15 minutes until they are slightly underbaked. Remove the cookies from the oven and let them cool on the baking sheets for 10 minutes.