In a small saucepan, add ¾ cup/180 milliliters water and the diced ginger and bring to a boil over high heat. Reduce to a very gentle simmer and cook for 5 minutes, letting the flavors infuse. Turn off the heat, cover with a lid and let steep for 10 minutes.
Place a fine-mesh sieve over a small liquid measuring cup and strain mixture, pressing with a rubber spatula to extract the salabat. (You should have ½ cup/120 milliliters. If you have less, add water.) Let cool for 10 minutes.
Heat oven to 350 degrees. Grease a 9-by-5-inch loaf pan with butter and line with parchment paper, leaving overhang on long sides
Prepare the cake: In a medium bowl, whisk together flour, ground ginger, salt, baking powder and baking soda.
In a large bowl, whisk together cooled salabat, honey, oil, sugar, sour cream, eggs, lemon zest, lemon juice and vanilla. Add flour mixture all at once and whisk until just combined. The batter will look like pancake batter.
Scrape the batter into the prepared loaf pan. Bake until golden and a wooden skewer inserted into the cake’s center comes out clean, about 1 hour. Cover loosely with foil for the last 10 minutes of baking to prevent overbrowning.
Transfer the pan to a wire rack set inside a foil-lined sheet pan (this will catch the glaze later) and let cool for 20 minutes. Using parchment overhang as handles, lift cake onto wire rack. Discard parchment and let cake cool completely.
Make the glaze: In a small bowl, whisk together the powdered sugar, honey, lemon juice and 1 teaspoon water. Drizzle glaze down the center of the cooled cake and spread outward, letting gravity pull long drips down the sides. Top with crystallized ginger. Let glaze set before slicing and serving.