Prepare an 9 x 13-inch pan by greasing and generously dusting with confectioners’ sugar.
Sprinkle unflavored gelatin over 3/4 cup of cold water in the bowl of an electric stand mixer; set aside while making the syrup.
In a medium saucepan, combine granulated sugar, corn syrup, salt and 1/2 cup water. Cook over medium heat until the mixture reaches 240 degrees F, soft ball stage.
Using the whisk attachment and with the mixer on low speed, slowly pour the hot sugar syrup into the dissolved gelatin. Turn the mixer to high speed and whip until very thick. This will take about 15 minutes. Add vanilla and peppermint extract and mix thoroughly.
Pour mixture into the prepared pan, using a lightly oiled spatula. Spread evenly, and lightly press half of the crushed peppermint candies into the top of the mixture. Dust top with powdered sugar and let stand uncovered overnight allowing it to dry out.
Turn marshmallows onto a cutting board. Using a lightly oiled knife or scissors, cut into squares. Press peppermint pieces into the sides of the marshmallows. Dust with more confectioners' sugar to keep them from sticking together.
Cook's Note: Using scissors, cut marshmallows into 1-inch cubes for hot cocoa & coffee. Cut into large squares and insert a candy stick, wrap in a cellophane bag and tie with a ribbon for gift giving.
Store any leftovers in an airtight container for up to one week.