Beat sugar and butter until pale (2-3 minutes), then beat in egg. Add flour, baking powder and ½ teaspoon fine sea salt, and beat to combine. Stir in sesame seeds and peanuts. Refrigerate until firm (1 hour).
Preheat oven to 160C and line 2 oven trays with baking paper. Roll tablespoonfuls of dough into balls, place on trays and press lightly to flatten. Bake, swapping trays halfway, until golden and crisp (12-15 minutes). Cool on trays for 5 minutes, then cool completely on a wire rack. Biscuits will keep for 2 days in an airtight container.