In a 3- to 4-quart pan, combine white rice, wild rice, broth, rice wine, salt, chili flakes, ginger, garlic, and 1 cup water. Bring to a boil over medium-high heat. Cover and reduce heat to a bare simmer. Cook (without stirring) until the white rice has disintegrated into a thick, oatmeal-like porridge and the wild rice has split open and is very tender, about 45 minutes.
Ladle into deep bowls and top with baked tofu, green onions, cilantro, and fried shallots to taste.