Remove the mango sorbet and ice cream from the freezer 10 minutes beforehand to allow them to soften. Line a 9x9 inch baking pan with plastic wrap or parchment paper.
Distribute spoonfuls of half of the mango sorbet onto the bottom of the baking pan. Dollop spoonfuls of half of the vanilla ice cream in the blank spaces. Use a spoon to flatten the layer and swirl the flavors together. Repeat this process with the remaining sorbet and ice cream to create another layer of marbling. Cover the baking pan with plastic wrap and place the ice cream into the freezer to solidify for at least 3-4 hours.
Heat a pan over medium heat. Add in the unsalted butter and allow it to melt. Once it has melted, continue cooking for another 7-9 minutes until the butter has turned a light golden brown color. Set it aside to cool for 15 minutes.
Add the all purpose flour, kosher salt, baking soda, and cinnamon to a bowl. Mix with a whisk until the ingredients are evenly distributed.
In a separate large bow, pour in the browned butter, brown sugar, and granulated sugar. Mix until combined then add in the egg and vanilla extract. Whisk until homogenous then pour in the dry ingredients. Gently fold everything until it forms into a ball of dough.
Cover the bowl with plastic wrap and place it in the fridge for 30 minutes. Preheat the oven to 375˚F. Line a few baking sheets with parchment paper. Set aside.
Scoop balls about 2 tablespoons in size and place them onto the lined baking sheet, spacing them 1½ inches apart. Bake the cookies in the oven for 10-11 minutes until the edges are set but the center is still soft. When you remove the cookies from the oven, firmly tap the bottom of the baking sheet onto the surface so that the cookies crinkle and flatten. Sprinkle flakey salt on top
Allow the cookies to cool on the baking sheet for about 8-10 minutes before transferring to a wire rack to cool completely.
Remove the ice cream from the freezer. Have a bowl of hot water next to you. Dip a 3-inch ring cutter into the hot water for a few seconds. Remove it then press it into the sheet of ice cream to cut out circles. Alternatively, you can use any ring cutter that is around the same size as your cookies or a glass and cut around the perimeter with a knife.
Layer the cut out ice cream onto the bottom of one cookie then sandwich it with another. Enjoy!