Prepare Gelatin: Mix gelatin powder with 2 tablespoons water in a small bowl. Add vanilla extract or scrape seeds from a vanilla bean into the mixture but do not stir.
Cook Syrup: In a 1-quart pot, combine ¼ cup water, corn syrup, sugar, and salt. Stir and heat over medium heat until bubbling at the edges (about 3 minutes). Increase to medium-high heat, attach a digital thermometer, and cook without stirring until the temperature reaches 250°F (approximately 4 minutes).
Cool and Whip Base: Transfer the hot syrup to a heatproof bowl, scraping out all syrup. Let it cool to exactly 212°F (about 4 minutes). Add the gelatin mixture. Use a hand mixer on medium-high speed to whip until thick, snowy white, and tripled in volume (around 10 minutes).
Incorporate Butter: Add softened butter in 5-6 additions, whipping thoroughly after each. Scrape the bowl to ensure a smooth mixture. Transfer to a greased container and let stand at room temperature until firm (approximately 2 hours).
Homemade Cool Whip Variation: Omit butter. Mix milk and powdered milk in a small bowl. Add to the marshmallow mixture and transfer to a stand mixer. Add heavy cream and whip on medium-low, gradually increasing to medium-high, until thick and creamy.