Combine sugar, corn syrup, water, and salt in a heavy saucepan
Cook over medium heat, stirring until the sugar dissolves
Stop stirring and boil until the mixture reaches hard crack stage, about 300°F to 310°F
Remove from heat and quickly stir in butter and vanilla if desired
Add baking soda if making a lighter, aerated brittle
Stir in nuts, such as peanuts or almonds, if using
Pour the mixture onto a greased or parchment-lined baking sheet
Spread it thinly with a spatula
Let it cool completely until hard
Break into pieces and store in an airtight container