In a medium saucepan over low heat, melt the butter. Once melted, continue to cook until it turns golden brown. Swirl the pan occasionally so that it browns evenly. Watch fairly closely, as it can go from brown to burned quickly. When the color has turned golden, remove from heat and poor into a shallow dish. Let cool to room temperature.
Preheat oven to 375 degrees and line a sheet pan with parchment paper.
Beat the brown butter, sugar, and brown sugar on medium high speed with an electric mixer for about 2 minutes. Add the egg and vanilla extract.
In a separate bowl, combine the flour, baking soda, and salt. Add to the wet ingredients and mix until just combined. Add the chocolate chips and mix until incorporated.
Spoon by the tablespoon onto the prepared baking sheet, leaving 2 inches in between each cookie. Sprinkle with coarse salt. Bake until golden brown, 12-14 minutes. Let cool on a wire rack for 5 minutes.
To assemble s’mores sandwiches, turn oven down to 350 degrees.
Take half of the cookies and place them bottom side up on the same sheet pan that was lined with parchment paper.
Break the chocolate bars up, covering the cookie. Place marshmallows on top of chocolate.
Bake in oven for about 5 minutes until the marshmallows start to melt.
Remove from oven and sandwich both halves of the cookies together. Let cool slightly and serve.