Line an 8x8 inch baking pan with parchment and lightly spray with non-stick cooking spray.
In a small sauce pan over medium heat, melt butter. Continue cooking butter, stirring frequently and adjusting heat as needed, until butter becomes a golden brown color and smells nutty, about 2-3 minutes. Remove from heat and let cool.
Add cold water to the bowl of a stand mixer and sprinkle gelatin over the top. Stir a little to combine, and allow gelatin to bloom while you make the syrup.
Meanwhile, start the syrup. In a heavy bottomed saucepan, add both sugars, corn syrup, salt, and water. Bring to a boil over medium to medium high heat. Once boiling, do not stir. Place a lid on the mixture, and allow to boil gently for about 2-3 minutes until sugar is dissolved. Remove lid and check temperature with a candy or food thermometer. Continue to gently boil without stirring until temperature reaches 242 degrees F. Remove from the heat, and allow for cool for about 1-2 minutes until no longer bubbly.
Turn your mixer (with the bloomed gelatin mixture) to a medium speed. Carefully pour the syrup mixture into the gelatin in a slow, steady stream along the side of the bowl. Once all the syrup is added, increase speed to medium high. Continue to beat until marshmallow is very light and fluffy and cool to the touch.
Add vanilla extract and mix to combine. Very gently add a few large spoonfuls of the marshmallow mixture to your cooled brown butter, stirring to incorporate. Add this back to the rest of your marshmallow mix, gently folding until combined, being careful not to deflate the marshmallow mixture (I fold in until just swirled through). Pour mixture into prepared pan, and spread evenly.
To dust the marshmallows, sift together confectioner's sugar and cornstarch in a medium bowl. Using the sifter, dust some of the mixture over the top of the marshmallow in a thin even layer. Let sit at least 4 hours or overnight to set. Reserve remaining dusting powder.
Remove marshmallows from the pan onto a cutting board lightly dusted with cornstarch mixture. Cut into squares. Gently toss cut marshmallows with dusting powder (in batches) to lightly coat cut sides. Serve or store in an airtight container.