Chicken with Ginger Beet Noodles

Name: Chicken with Ginger Beet Noodles
Ingredients: 1 pound spiralized beets; 3 tablespoons rice vinegar; 2 tablespoons low-sodium soy sauce; 2 tablespoons grated peeled fresh ginger; 2 cloves garlic, grated; 1 large serrano chile pepper, thinly sliced (seeded for less heat); 4 skinless, boneless chicken breasts (about 8 ounces each); Kosher salt and freshly ground pepper; 1/4 cup toasted sesame oil; 8 ounces shiitake mushrooms, stems removed; Sliced scallions and fresh mint, for topping