How to Make It
Rub an 18- x 13-inch baking sheet lightly with butter, or coat with cooking spray. Set aside.
Stir together sugar, water, corn syrup, and fine sea salt in a heavy, 2-quart saucepan; attach a candy thermometer to side of pan. Place pan over medium-high, and cook, occasionally stirring gently with a wooden spoon, until sugar dissolves and mixture boils. Once sugar syrup is clear and thickened, cook, undisturbed, until the thermometer reaches 230˚F to 235˚F (soft-ball stage), 5 to 7 minutes.
Stir in butter, and continue cooking over medium-high, stirring occasionally, until butter melts, syrup starts to caramelize, and the thermometer reaches 300˚F to 305˚F (hard-crack stage), 6 to 8 minutes. Immediately remove pan from heat; working very quickly, vigorously stir in the mixed nuts and peanuts just until completely coated in caramelized syrup.
Immediately stir in baking soda and vanilla. Once the baking soda hits the hot, caramelized syrup, it will lighten and start to get foamy. As soon as ingredients are combined, pour hot candy onto prepared baking sheet. Using the back of a wooden spoon, quickly and gently spread mixture, pushing into a fairly thin layer that covers most of baking sheet. (A few holes are fine. It doesn’t need to be a solid sheet of candy.) Quickly sprinkle entire surface with flaky finishing salt. Let stand until brittle hardens, about 1 hour. Break into pieces. Store brittle in an airtight container or a ziplock plastic bag for up to 2 weeks.
For a thinner, more delicate brittle, you can “stretch” it: After spreading the brittle onto the baking sheet, cool slightly for a minute or two just until the candy is pliable but still too hot to touch with your bare hands. Run a long, thin spatula under the candy to loosen it from the baking sheet, and (wearing clean rubber gloves) lift the edges and gently pull and stretch the candy. Move into the middle, pulling gently without tearing it, to make the brittle slightly thinner. You can leave it on the baking sheet to do this, stretching over the sides of the pan, or turn it out onto a marble or granite countertop or cutting board to make it easier to work with.