In a medium-sized bowl, mix together the soy sauce, sesame oil, brown sugar, and garlic. Add a pinch of kosher salt and black pepper. Add the beef and toss until evenly coated. Marinate for about 20 minutes.
If your rice cakes are frozen, soak them in a bowl of cold water to thaw.
Meanwhile, in a large skillet, heat a couple of tablespoons of cooking oil over medium high heat. Add the mushrooms, pepper, and onions. Cook until the onions start turning translucent. Add the beef and cook until it starts turning brown.
Add the rice cakes and evenly distribute in the skillet. Add the chicken broth, the spinach, cover, and bring to a high simmer. Uncover and stir. The rice cakes should be close to done. You can test by biting or cutting into one of them. If it cuts easily, it is done. You want it to be al dente - not too hard and not too soft. If it's mushy, it is overcooked.
Give it a quick stir and serve hot. Season with salt and black pepper to taste.