Line an 8x8 square baking dish with parchment paper and dust with ¼ cup powdered sugar.

In the bowl of your stand mixer with the whisk attachment, sprinkle 3 tablespoons agar powder over ½ cup cold water. Slowly mix until agar powder has dissolved.

In a large saucepan, combine the remaining ½ cup water with 2 cups sugar, 1 cup light corn syrup, and ⅛ teaspoon salt. Bring to a boil, without stirring, until a candy thermometer reads 240°F.

Remove from heat and carefully transfer to the stand mixer. Beat on high speed until the mixture is thick, about 10-15 minutes. Mix in ½ teaspoon peppermint extract.

Transfer to the prepared baking pan immediately and let sit uncovered for at least 12 hours. Once the tops are completely dry, place in refrigerator for 1 hour.

Once chilled, lift marshmallows out of the pan and slice into bite-sized pieces with a sharp, clean knife. Coat each marshmallow with remaining ¼ cup powdered sugar.