Packaging tip: Any plain gift box with a lid will feel decadently special when you wrap the lid and bottom separately.
Butter two large baking sheets; set the baking sheets aside.
Butter the sides of a heavy 3-quart saucepan. Add sugar, corn syrup, and water; stir to combine. Cook and stir over medium-high heat until the mixture boils. Clip a candy thermometer to side of the pan. Add the peanuts; cook over medium-low heat, stirring occasionally, until thermometer registers 280 degree F to 285 degree F (soft-crack stage; about 45 minutes).
Remove from heat; remove the thermometer. Quickly sprinkle baking soda and salt over mixture, stirring constantly until foaming subsides.
Immediately pour candy onto the prepared baking sheets. Spread as thinly as possible, using greased spoons or two greased forks to pull mixture. Cool.
Break candy into pieces. Store at room temperature in an airtight container. Makes about 1-3/4 pounds.