Butter the sides of a heavy 2-quart saucepan. Put the sugars, salt, corn syrup, milk, and butter in saucepan. Over medium heat, stir mixture constantly with a wooden spoon until sugars have dissolved and mixture comes to a boil. Continue to cook to a soft ball stage, approximately 236 degrees F on a candy thermometer. (If you do a cold water test, drizzle a drop of candy into a glass of cold water, the ball of candy will flatten between your fingers when you take it out of the water.) Remove from heat and allow it to cool for 10 minutes.
Add the vanilla and nuts, and beat with a spoon by hand for approximately 2 minutes or until candy is slightly thick and begins to lose its gloss. Quickly drop heaping tablespoons onto waxed paper. If the candy becomes stiff, add a few drops of hot water.