Stir flour, salt, lemon peel, and thyme together in a medium bowl. With your fingertips, rub butter into the dry ingredients until a coarse, crumbly mixture forms. Blend lightly beaten egg, egg yolks, and water together. Reserve 1 tablespoon of egg mixture for brushing. Make a well in center of flour. Add remaining egg mixture and blend together with your hands without kneading the dough together; dough will look a bit crumbly. Turn dough out onto a lightly floured work surface. Knead dough together once or twice, just until it sticks together. Press dough into a 1-inch disc, wrap in plastic film, and refrigerate until firm, about 1/2 hour. Preheat oven to 350° and line bottom of a baking sheet with parchment paper or a nonstick baking mat. Remove dough from refrigerator, unwrap, and place it on floured work surface. Press dough into a 6-by-5-inch rectangle. With rolling pin, roll dough into a larger 10-by-7-inch rectangle, about 1/4 inch thick. Cut dough in half, forming two 5-by-7-inch pieces. Using a pizza wheel or sharp paring knife, cut into 1/2-inch-wide strips. Carefully place strips on prepared baking sheet leaving a little room between each cookie. Brush tops with reserved egg mixture and sprinkle a little coarse sea salt on top. Gently press salt into the surface of each cookie so it does not fall off. Bake until lightly browned, about 20 minutes. Transfer to cooling rack and serve warm or at room temperature. Store in an airtight container at room temperature for up to 1 week.