Cauliflower Fried Rice

Name: Cauliflower Fried Rice
Ingredients: 1 medium head cauliflower (about 1 3/4 pounds), stems discarded, cut into 1-inch florets; 1 tablespoon plus 2 teaspoons peanut oil, plus additional for oiling the pan; 2 large eggs, well-beaten; 4 ounces fresh shiitake mushrooms, stems discarded, sliced into 1/4-inch pieces; 6 scallions, thinly sliced, 1 tablespoon reserved; 1/4 cup coarsely grated carrot (from about 1 carrot); 1 large garlic clove, minced; 1 1/2-inch piece ginger, peeled and minced; 2 tablespoons soy sauce; 2 teaspoons toasted sesame oil; Kosher salt; 1/2 cup frozen peas, defrosted in a strainer at room temperature and rinsed