Mushroom YouFan (Taiwanese Sticky Rice)

Name: Mushroom YouFan (Taiwanese Sticky Rice)
Cuisine: Asian, Chinese
Ingredients: 10 large dried shiitake mushroom caps; 2 Tbsp. small dried shrimp (optional); 2 Tbsp. vegetable oil; 1 2" piece ginger, peeled, thinly sliced; 2 cups long- or short-grain glutinous rice (such as Koda Farms Superior Short Grain Sweet Rice), rinsed; ¼ cup store-bought or homemade fried shallots; ¼ cup dry rice wine (such as michiu or sake); 2 Tbsp. black sesame oil or toasted sesame oil, plus more for serving; 2 Tbsp. Kimlan aged soy sauce or regular soy sauce; ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt; 1 tsp. freshly ground white pepper; 1 bunch cilantro, coarsely chopped