Step 1: Prepare your workstation. Lightly butter a large, heat-proof platter, a marble slab, or a large baking sheet. Have a candy thermometer clipped to your heaviest saucepan.
Step 2: In a large, heavy-bottomed saucepan, combine the granulated sugar, heavy cream, corn syrup, and salt. Stir over medium heat until the sugar has completely dissolved.
Step 3: Increase the heat to medium-high and bring the mixture to a boil. Insert your candy thermometer and cook without stirring until the thermometer registers 242°F (117°C).
Step 4: Immediately remove the saucepan from the heat. Stir in the unsalted butter and vanilla extract until fully melted and incorporated.
Step 5: Carefully pour the hot candy mixture onto your prepared buttered surface. Do not scrape the bottom or sides of the pan. Allow to cool undisturbed until it's warm enough to handle but not too hot, typically around 110-120°F (43-49°C).
Step 6: Generously butter your hands (or wear food-safe gloves). Begin to gather the candy from the edges towards the center. Start pulling the candy, stretching it out and folding it back on itself. Repeat this motion for 15-20 minutes, or until the candy is light in color and has a firm, taffy-like consistency.
Step 7: Once sufficiently pulled, stretch the candy into a long rope, about ½ to ¾ inch thick. Using buttered kitchen shears or a sharp, buttered knife, cut the rope into bite-sized pieces, approximately 1-inch lengths.
Step 8: Dust the cut pieces lightly with powdered sugar to prevent sticking. Store the candy in an airtight container at room temperature, separating layers with parchment paper if desired.