In a small bowl, combine 1/2 tablespoon teriyaki seasoning and 2 tablespoons canola oil. Place the mushroom caps onto a baking sheet and brush them with the oil mixture. Bake until they soften, about 15 minutes.
While the mushrooms are baking, heat the remaining 2 tablespoons canola oil in a large skillet or wok over medium-high heat. Add the chopped mushroom stems, scallion, ginger, and garlic and cook for 2 minutes. Add the ground pork and cook until cooked through, about 5 minutes. Stir in the soy sauce and the remaining teriyaki seasoning. Add the rice and cook until heated through.
Stuff the mushroom caps with the rice mixture. Transfer to a platter, garnish with cilantro, and serve immediately.