Prepare the Gelatin Base: In a small bowl, combine gelatin with ½ cup water and vanilla extract (if using). If using a vanilla bean, split and scrape out seeds, then add them to the gelatin mixture. Do not stir.
Cook the Syrup: In a 3-quart stainless steel pot, combine ½ cup water, sugar, corn syrup, and salt. Heat over medium, stirring until bubbling (about 5 minutes). Attach a digital thermometer and cook without stirring until the syrup reaches 250°F (about 5 minutes).
Combine Syrup and Gelatin: Transfer the hot syrup to a stand mixer bowl, scraping the pot thoroughly. Cool to 212°F (approximately 6 minutes), then add gelatin mixture. Mix on low until gelatin melts.
Whip Marshmallows: Gradually increase speed to medium-high and whip until the mixture becomes white, fluffy, and triples in volume (about 10 minutes). Reduce speed to low, add melted butter, and beat for a few seconds more.
Shape the Marshmallows: Spread the mixture into a greased 8-inch square pan, smoothing the top. Cover and refrigerate until firm, about 2 hours or overnight at room temperature.
Cut and Coat: Dust powdered sugar over the surface, invert onto a cutting board, and cut into 1½-inch cubes. Toss cubes in powdered sugar to coat, and store in an airtight container.