Line a baking sheet with a silicone baking mat or a piece of foil lightly greased with canola oil spray.
Combine the sugar, corn syrup and water in a medium saucepot fitted with a candy thermometer. Bring to a boil without stirring; cook until the mixture reaches 305 degrees F (the hard-crack stage), 12 to 15 minutes -- the sugar will become deeply caramelized.
Remove the pot from the heat and carefully add the butter, baking soda, vanilla paste and fennel; the sugar will bubble up and incorporate all the ingredients on its own. With a heatproof rubber spatula, stir in the pistachios and then immediately spread the mixture onto the prepared baking sheet in an even layer. While the brittle is still hot, zest the orange evenly over the top and sprinkle with flaky sea salt.
Let the brittle cool completely before breaking into small pieces. Serve immediately or store in an airtight container at room temperature. For longer storage, place the brittle in a zip-close bag, remove any excess air, and freeze for up to 1 month.