Separate egg whites into a clean mixing bowl; add cream of tartar and begin beating to soft peaks.
In a heavy saucepan combine sugar, corn syrup, water and salt; stir until dissolved.
Attach a candy thermometer and bring the syrup to a rolling boil without stirring.
Heat the syrup to 240°F (soft-ball stage).
As syrup nears 240°F, beat the egg whites at medium-high speed until stiff but not dry.
With the mixer running on low, slowly pour the hot syrup in a thin stream into the whipped egg whites.
Increase mixer speed and continue beating until the mixture is thick, glossy and holds shape.
Fold in the chopped toasted pecans and vanilla gently but quickly.
Drop spoonfuls onto parchment or waxed paper and press a pecan half on top of each piece.
Allow candies to set at room temperature until fully firm (about 2 hours) before storing or packaging.