Brush the bottom and sides of a 9-inch square baking pan with vegetable oil. Then, dust the pan generously with some confectioners' sugar by putting it through a fine mesh sieve. Knock out any excess sugar.
In the bowl of a stand mixer, fitted with whisk attachment, add ½ cup water. Sprinkle gelatin over the top of the water and stir to make sure it all comes in contact with water. Set aside to soften.
In a heavy 3- or 4-quart saucepan over medium heat, combine granulated sugar, corn syrup, and salt. Bring mixture to a boil, stirring until sugar is dissolved. Continue to boil without stirring until a candy thermometer reaches 240 degrees (soft ball stage). If the mixture bubbles up, turn down the heat a bit.
Remove saucepan from heat and let stand briefly until bubbles begin to dissipate.
While mixer is on low speed, pour hot sugar syrup into the softened gelatin by drizzling it in a thin stream down the side of the bowl.
Gradually increase mixer speed to high and beat until marshmallow gets thick and forms a thick ribbon when whisk is lifted, about 5 minutes.
Beat in the mint and vanilla extracts. Beat in a few drops of green food coloring or a mixture of blue and yellow food coloring, if desired (I used 6 drops yellow and 2 drops blue from Wilton's Color Right line).
Working quickly to prevent hardening, scrape marshmallow into the prepared pan (it will be very sticky) and use wet fingertips to make sure it's even and smooth on top.
Let baking pan stand at room temperature and uncovered for at least 4 hours, but ideally overnight. The surface should no longer be sticky and you should be able to gently pull marshmallow away from the sides of the pan with your fingertips.
Dust a cutting board with confectioners' sugar and use a rubber spatula to pull the sides of the marshmallow from the edge of the pan. This may take a bit of work and you may need to also use the spatula to loosen the marshmallow from the bottom of the pan. Invert marshmallow onto cutting board and dust the top with confectioners' sugar.
Using a long thin knife brushed with vegetable oil and dusted with confectioner's sugar, cut marshmallow lengthwise into 6 strips, then crosswise into sixths (you should get about 36 squares total) or into a different size of your choice.
Coat marshmallows, one at a time, in confectioners' sugar and use a pastry brush to brush off any excess.
Store marshmallows in an airtight container layered between sheets of wax paper or parchment paper in a cool, dry place for up to a month.