Vegetable-oil cooking spray
2 cups sugar
1 tablespoon light corn syrup
4 packages (1/4 ounce each) unflavored gelatin
3/4 teaspoon peppermint extract
2 large egg whites
2 teaspoons red food coloring
Coat an 8-inch square pan with cooking spray; line bottom with parchment paper. Coat the parchment with cooking spray, and set pan aside. Put sugar, corn syrup, and 3/4 cup water in a small saucepan. Cook over medium heat, stirring, until sugar is dissolved. Stop stirring; let mixture come to a boil. Raise heat to medium-high; cook until mixture registers 260 degrees on a candy thermometer.
Meanwhile, sprinkle gelatin over 3/4 cup water in a heatproof bowl; let stand 5 minutes to soften. Set the bowl with the gelatin mixture over a pan of simmering water; whisk constantly until gelatin is dissolved. Remove from heat, and stir in extract; set aside.
Beat egg whites in the bowl of an electric mixer fitted with the whisk attachment until stiff (but not dry) peaks form. Whisk gelatin mixture into sugar mixture; with mixer running, gradually add to egg whites. Mix on high speed until very thick, 12 to 15 minutes.
Pour mixture into lined pan. Working quickly, drop dots of red food coloring across surface of marshmallow. Using a toothpick, swirl food coloring into marshmallow to create a marbleized effect. Let marshmallow stand, uncovered, at room temperature until firm, at least 3 hours or overnight. Cut into squares.