Line a square pan (I used 8x8 inch) with plastic wrap and then grease it well with the oil. Set aside.
In mixing bowl, sprinkle the gelatin (make sure it's not clumped together) into 1/2 cup of VERY cold water. Barely stir it just enough that all the gelatin is wet. Soak it for about 10-12 minutes.
Combine the sugar, corn syrup and remaining 1/2 cup water in a saucepan and whisk only til just mixed. Don't overstir. Bring it to a strong, hard boil and then keep boiling until it is 240 degrees (or soft-ball stage), and then remove from heat. It's important to reach the proper temperature, so use a candy thermometer unless you've mastered identifying soft-ball stage.
Next, you are going to pour this super hot mixture into the gelatin mixture. But be careful - I spilled this on my hand decades ago and it's quite an unforgettable experience! So, pour this in slowly and carefully. Whisk, increasing speed to high, for about 10-15 minutes. You can use a hand mixer (if you have a lot of patience) or a stand mixer. After the mixture is nice and fluffy but stiff, beat in the vanilla extract.
Coat your hands and a spatula with vegetable oil. Pour the marshmallow mixture into your prepared pan and smooth with spatula. Place a piece of oiled plastic wrap over it and press down with your hands. Let set for at least four hours at room temperature.
So here's the fun part. Cover a surface with confectioner's sugar combined with the cornstarch and flip the marshmallows onto the surface. Coat the entire block with the confectioner's sugar mixture. Next, coat a knife with the sugar/cornstarch combo and cut the marshmallows into pieces. Then coat the marshmallow pieces with the mixture. This will keep nicely in an airtight container or plastic bag for 2-3 weeks.
Optional add-ins (add when you stir in the vanilla): For pink marshmallows, add a few drops of red food coloring. For chocolate marshmallows, add 1/4 cup cocoa powder. For peppermint, add 1-2 teaspoons of peppermint extract.