Line a baking sheet with parchment paper; lightly spray with cooking spray.
In a large stainless-steel saucepan, combine sugar, corn syrup, ½ cup water, and salt, stirring just until moistened. Cook over medium-high heat, without stirring, until a candy thermometer registers 260°, 10 to 12 minutes. When mixture reaches temperature near 240°, continue to next step.
In the bowl of a stand mixer fitted with a whisk attachment, beat egg whites and cream of tartar on high speed until stiff peaks form. When sugar mixture has reached 260°, slowly pour mixture into egg whites in a slow steady stream while beating. Beat on high speed until mixture holds its shape and begins to lose its gloss, 6 to 9 minutes. Immediately reduce speed to low, and add in chopped pecans and vanilla, beating just until combined.
Working quickly with 2 spoons or a small spring-loaded scoop, immediately drop mixture by tablespoonfuls onto prepared pan. Gently press a pecan half on top of each candy. Let stand until dry and can easily be removed from pan, about 6 hours. Candies can be stored in an airtight container at room temperature for up to 2 weeks.
Notes
After the sugar mixture is added to the beaten egg whites, the mixer will sound like it has slowed down. This is normal as the mixture becomes very thick. When the mixture is almost ready to add the pecans and extract, you will hear the mixer increase in pitch and speed. Check to make sure the mixture has lost its gloss, looks dry, and holds its shape before adding them. Then, get your spoons ready to scoop!
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/old-fashioned-divinity-candy/