Place a pot of water (or the bottom of a double boiler) on the stove top and bring to a simmer.
In the bowl of a stand mixer, whisk together the egg whites and sugar until frothy, about 1 minute.
Place the bowl of egg whites over the pot of simmering water and cook, whisking constantly, until the mixture reaches 160 degrees, about 8-10 minutes. Alternatively, you can take a small drip (cooled slightly!), and rub it between your fingers. If it feels grainy, it needs a little longer. You want the sugar to be completely melted.
Pour the egg white mixture into the bowl of an electric stand mixer fitted with the whisk attachment. Beat at high speed until soft peaks form, about 5-7 minutes. The mixture should hold its shape for a few seconds before flopping over.
Allow to cool to room temperature (it should be close already after beating), then switch to the paddle attachment. Add the butter a few Tablespoons at a time, beating well and making sure it is entirely incorporated before adding more.
Add the marshmallow creme, salt, and peppermint extract and mix well. Taste, and add additional peppermint if desired.
Assemble:Place the frosting into a piping bag fitted with a large round tip or a gallon zip lock with a small slit cut out of the end. Swirl a layer of filling on half of the cookies and sandwich with the second cookie.
Spread the crushed peppermint out over a baking sheet then roll the exposed edges of the filling in the peppermint.