Put the flour and thyme in a bowl or food processor. Add the butter and rub in with the fingertips or process until the mixture resembles breadcrumbs. Stir in the cheese and egg yolk and mix or blend to a dough.
Knead the dough on a lightly floured surface until smooth, then roll out to 5 mm (¼ inch) thick. Trim the edges and cut into sticks 5 mm (¼ inch) wide and about 9 cm (3½ inches) long. Place slightly apart on a greased baking sheet.
Sprinkle with sea salt and bake in a preheated oven, 200°C (400°F), Gas Mark 6, for about 15 minutes until golden. Leave to cool slightly on the sheet, then transfer to a wire rack to cool completely. Serve scattered with extra thyme.