Making this traditional Southern candy works best on a dry day; too much humidity prevents it from setting. For best texture, work quickly when scooping the candy. If it's setting too quickly, stir in a few drops of hot water until smooth.
In a medium saucepan, combine sugar, corn syrup, and 1 cup water. Bring to a boil, stirring just until sugar dissolves, and cook until syrup reaches 250 degrees (firm-ball stage) on a candy thermometer.
Meanwhile, in the bowl of a stand mixer fitted with the whisk attachment, starting on low and gradually increasing to high, beat egg whites with salt until stiff peaks form. If peaks form before the syrup reaches 250 degrees, reduce speed and keep mixer running on low.
With the mixer on medium speed, add the syrup in a slow, steady stream (taking care not to hit the whisk or side of the bowl). Add vanilla. Increase speed to high and continue to whisk until mixture holds it shape and begins to lose its gloss, 10 to 20 minutes. Prepare a small bowl of hot water for dipping and a 1-tablespoon cookie scoop or two spoons; line up miniature candy cups on a baking sheet.
Working quickly, use cookie scoop or spoons to drop 1 heaping tablespoon candy into each cup, dipping scoop into hot water as needed to prevent sticking. Press pecans into candy. Let candy cool completely, at least 6 hours and up to overnight. Candy can be stored in an airtight container at room temperature up to 1 week.