Line a large cookie sheet with parchment paper and set aside.
In a large saucepan, heat together the sugar, water, corn syrup and salt. Cook on medium heat, stirring occasionally, for about 7-10 minutes or until the temperature reaches 260 degrees F. on a candy thermometer. Just before the candy reaches temperature, beat the egg whites on high speed using an electric mixer or stand mixer until stiff peaks form.
Remove the boiling candy from the heat and, with the mixer on high speed, stream in the hot candy VERY slowly. It should take you at least 2 or so minutes to fully pour the hot candy mixture into the egg whites. Continue beating the mixture until it's no longer glossy and it holds its shape, about 6-10 minutes (it depends on your mixer). Stir in the chopped pecans and vanilla extract until combined.
Butter two spoons (or grease them lightly with cooking spray) and, working quickly, drop rounded Tablespoonfuls of the divinity mixture onto the parchment-lined baking sheets. You may need to scrape the candy mixture off of one spoon with the other spoon, then quickly flick your wrist to create a soft curl (like soft serve) on top of the candy. It's okay if you don't get it quite right!
Allow the candy to set at room temperature - maybe overnight, depending on the humidity in your home - until dry to the touch and no longer sticky. Once set and dry, you can keep it at room temperature for up to 5 days in an airtight container.
NOTES: It is totally okay to take a small teaspoon-sized spoon of candy and test it on the parchment before doing the larger scoops. The divinity is ready when it holds its shape in a mound on the parchment paper. If it turns into a puddle, continue beating the mixture.