In a large bowl, combine broccoli, red bell pepper, snow peas, and shallots. Stir together the grated ginger, soy sauce, sesame oil, and olive oil. Pour the oil mixture over the vegetables and toss until everything is well combined. Spread into an even layer on a sheet pan and roast in the oven for 30 minutes, stirring once halfway through cooking.
Heat a medium frying pan over medium-high heat. Add the coconut oil. Once the coconut oil is melted, add the mushrooms. Cook the mushrooms for 2-3 minutes and then add soy sauce. Cook for another 5-7 minutes until the mushrooms start taking on some brown color. Add the bulgogi and saute until the meat is cooked through.
To serve, scoop rice into a bowl. Top with roasted vegetables, beef, and mushrooms. Garnish with scallions, sambal, and hoisin sauce.