Heat water in a saucepan over medium-low heat; cook and stir white sugar into hot water until dissolved, about 5 minutes. Stir brown sugar and salt into the sugar mixture until dissolved; stir in butter.
Whisk eggs and vanilla together in a bowl until smooth; stir 2 to 3 tablespoons hot sugar mixture into eggs, 1 tablespoon at a time, to slowly bring eggs up to temperature without cooking them. Slowly stir egg mixture into saucepan of sugar mixture. Fold in pecans.
Increase temperature to medium heat; cook and stir mixture until thickened and bubbling, about 5 minutes. Reduce heat to low before serving.