Step 1Line a half-sheet pan or two quarter-sheet pans or other rimmed baking sheets with a nonstick baking mat (Silpat) or nonstick or regular foil. If using regular foil, lightly coat with nonstick cooking spray.
Step 2Arrange the crackers decorative side down (flat sides up) in a single layer with no gaps on the prepared pan, breaking crackers if needed to fit.
Step 3Combine the sugar, butter, and corn syrup in a large saucepan and set over medium heat. Cook, occasionally stirring gently, until the butter and sugar melt. Brush the insides of the saucepan with a pastry brush dipped in water to eliminate any sugar crystals. Continue cooking until the mixture starts to brown around the edges of the pan. Insert a candy thermometer and continue cooking, carefully stirring occasionally, until the candy is at the hard crack stage (the thermometer should register 310 degrees).
Step 4Remove the thermometer and immediately and carefully pour the toffee evenly over the crackers. If needed, gently spread in an even layer. Let cool for 2 minutes, then sprinkle the chocolate evenly over the toffee.
Step 5Let stand until melty, 1 to 2 minutes, then spread in an even layer. Scatter the hazelnuts evenly over the chocolate, then sprinkle with the sesame seeds. Press the nuts gently into the chocolate.
Step 6Carefully transfer the pan to the freezer and freeze until the toffee and chocolate are set, 10 to 15 minutes. Break into shards and serve.
Black and White Sesame Butter Toffee: Omit the hazelnuts. Scatter ½ cup white sesame seeds all over the chocolate along with the black sesame seeds.