Preheat oven to 350°F. and line 2 baking sheets with parchment paper. In a stand mixer, cream butter with brown sugar and molasses on high speed until incorporated, about 1 minute. Lower speed to medium. Add 1 whole egg and mix until incorporated. Add egg yolk and continue mixing until incorporated; scrape down the sides of the bowl as necessary. Add Bohemian Forest, baking soda, salt and half of the flour. Mix at medium speed until incorporated, scraping down the sides of the bowl again as necessary. Add water, lemon and orange zest, ¾ cup of the diced crystallized ginger, and remaining half of the flour and mix until dough just comes together.
Turn dough out onto a floured surface and knead for a minute until a smooth ball comes together. Divide dough in half and roll out each half into a ½-inch thick square. Cut dough into 2-inch squares or diamonds, or use a cookie cutter shape of your choice. Place squares about 1 inch apart on the prepared baking sheets.
Whisk egg white with lemon juice and confectioner's sugar. Using a pastry brush, brush a thin layer of glaze on each square. (For a nice crackle effect, glaze squares just before they go in the oven. You'll likely end up with leftover glaze.) Top each square with 2 to 3 pieces of the remaining diced crystallized ginger and sprinkle with lavender to taste. Bake one sheet at a time for 5 minutes then turn the sheet around in the oven and bake for 5 more minutes. Let squares cool on the baking sheets before serving. These will keep for up to 3 days stored in an airtight container.
Notes
Instead of rolling and cutting the dough into squares or other shapes, you can turn them into tablespoon sized drop cookies; the baking time will remain the same.