Preheat oven to 350°F. Spread pecan halves and chopped pecans on a baking sheet. Toast for 6-8 minutes or until fragrant. Set aside.
On the stovetop on low heat, cook sugar, corn syrup and water together in a heavy bottomed saucepan fitted with a candy thermometer. Stir constantly, just until sugar is dissolved. (If you continue to stir, the sugar may caramelize.)
Continue cooking, without stirring to 260°F on a candy thermometer, or hard ball stage. (Alternately, until a small amount of mixture dropped into very cold water forms a hard ball that holds its shape but, is still pliable.)
Meanwhile, beat egg whites in a medium-size mixing bowl using an electric mixer on high speed until stiff peaks form. (A stand mixer works best)
Lower speed to medium, Continue beating constantly while pouring hot syrup in a thin stream into egg whites. Add vanilla. Continue to beat on medium speed until mixture holds its shape, about 8-10 minutes. Gently stir in chopped nuts until evenly distributed.
Have nearby 3 large sheet pans lined with wax paper. Working quickly using a 1 Tbsp cookie scoop or Tbsp, Drop into even rounds on wax paper. Press one pecan half onto each. (Have a bowl of hot water nearby to dip scoop, if needed, then dry before continuing to form divinity)
Let dry completely at room temperature for 8-12 hours.
Store in an airtight container at room temperature, separate layers by wax paper for up to 2 weeks. Freeze in an airtight container for up to 2 months.