Step 1

Combine flours, sugar, lemon thyme and ¼ tsp flaked sea salt in a bowl. Rub in butter with your fingertips until it resembles coarse breadcrumbs. Combine oil and yolks in a bowl, then add to flour mixture and work into a dough by hand. Halve dough and roll each piece in baking paper to form 2 logs, twist ends and refrigerate until firm (1 hour).

Step 2

Preheat oven to 150°C and line baking trays with baking paper. Cut logs into 8mm-thick slices and bake on trays until golden brown (20-25 minutes). Cool completely on trays.

Step 3

For lemon icing, stir ingredients in a bowl until smooth and combined. Dip, drizzle or spoon over shortbread, scatter with extra lemon thyme and leave to set (10-12 minutes) before serving. Olive oil shortbreads will keep for up to a week stored in an airtight container.