Coconut, Ginger, and Mushroom Noodles

Name: Coconut, Ginger, and Mushroom Noodles
Cuisine: Asian
Ingredients: 2 Tbsp. granulated sugar; ½ cup plus 2 Tbsp. black (Chinkiang) vinegar or unseasoned rice vinegar; 6 Tbsp. light soy sauce, divided; 12 oz. shiitake mushrooms, stems removed, thinly sliced, divided; 1 5” piece ginger, peeled, cut into matchsticks, divided; ½ cup raw cashews; ½ cup unsweetened shredded coconut; 8 oz. dried soba noodles; 2 Tbsp. kecap manis (sweet soy sauce); 6 Tbsp. vegetable oil, divided; 12 canned baby corn, halved crosswise; 8 oz. green beans, trimmed, cut into thirds; 6 small shallots, thinly sliced