Ankake Tofu (Savory Dashi Sauce)

Name: Ankake Tofu (Savory Dashi Sauce)
Cuisine: Asian, Japanese
Ingredients: 1 block (300-350 g) soft or silken tofu; 1 1/2 cup (150-170 g) mushrooms (shimeji, beech, enoki or shiitake); 1/2 small carrot (30-50 g), thinly sliced; 1/4 cup (25 g) sliced scallions, whites and greens separated; 1 cup (250 ml) dashi stock of choice; 1 tbsp (15 ml) sake; 1 tbsp (15 ml) mirin; 1 1/2 (22 ml) tbsp soy sauce*; pinch of salt; 2-4 tsp (7-13 g) potato starch; 1 1/2 tsp (7 g) minced ginger; 1 tsp (5 ml) sesame oil, optional