1. Stir the flour, salt, lemon peel, and thyme together in a medium bowl.
2. With your fingertips, rub the butter into the dry ingredients until a coarse, crumbly mixture forms. Blend the lightly beaten egg, egg yolks, and water together. Reserve 1 tablespoon of the egg mixture for brushing.
3. Make a well in the center of the flour. Add the remaining egg mixture and blend together with your hands without kneading the dough together; the dough will look a bit crumbly.
4.Turn the dough out onto a lightly floured work surface. Knead the dough together once or twice, just until it sticks together. Press the dough into a 1-inch disc, wrap in plastic film, and refrigerate until firm, about 1/2 hour.
5. Preheat the oven to 180 degree centigrade and line the bottom of a baking sheet with parchment paper or a nonstick baking mat. Remove the dough from the refrigerator, unwrap, and place it on a floured work surface.
6. Press the dough into a 6-by-5-inch rectangle. With a rolling pin, roll the dough into a larger 10-by-7-inch rectangle, about 1/4 inch thick. Cut the dough in half, forming two 5-by-7-inch pieces.
7. Using a pizza wheel or sharp paring knife, cut into 1/2-inch-wide strips. Carefully place the cookies on the prepared baking sheet leaving a little room between each cookie.
8. Brush the tops with the reserved egg mixture and sprinkle a little coarse sea salt on top. Gently press the salt into the surface of each cookie so it does not fall off.
9. Bake until lightly browned, about 20 minutes. Transfer to a cooling rack and serve warm or at room temperature. Store the cookies in an airtight container at room temperature for up to 1 week.