Line a rimmed baking sheet with a silicone mat or parchment and lightly grease it with the vegetable oil. Lightly oil a heatproof spatula and keep the sheet near the stove.
In a 3- to 4-quart heavy saucepan, combine the granulated sugar, light corn syrup, and water. Cook over medium heat, stirring until the sugar dissolves and the syrup looks clear, 3–4 minutes; brush down the sides with a wet pastry brush if crystals form. Attach a candy thermometer.
Increase heat to medium-high and boil without stirring until the syrup reaches 300°F (hard crack), 10–15 minutes, and is deep golden amber. Immediately remove the pan from the heat.
Quickly stir in the unsalted butter and vanilla extract until melted and smooth. Stir in the unsalted roasted peanuts to coat, then sprinkle in the baking soda and kosher salt and stir just until the candy foams and lightens in color.
Immediately pour the foaming candy onto the prepared baking sheet and tilt to spread. Use the oiled spatula (or two forks) to quickly stretch and pull the brittle as thin as possible before it sets, working from the center outward.
Cool until completely hard, 15–30 minutes. Break into pieces and store airtight at room temperature for up to 2 weeks.