Heat a large skillet over medium-high heat and add the neutral oil. Add the onion and the white parts of the scallion, then cook for 2 minutes, stirring often, until the onion starts to soften and smell sweet.
Add the carrot and mushrooms and cook for 3 minutes. You are not trying to fully brown everything; you just want the mushrooms to give up a little water and the carrot edges to soften so they finish nicely in the sauce.
Pour in the sauce mixture and bring it to a steady simmer. Once it is bubbling, add the drained rice cakes and stir gently so they are coated and not clumped.
Simmer for 12 minutes, stirring every minute or so, until the rice cakes are chewy-tender and the sauce looks glossy and slightly thickened. Keep the heat at a lively simmer; too low and the sauce will not reduce, too high and it can stick before the rice cakes soften. If the pan looks dry before the rice cakes are tender, add 1/4 cup water and keep simmering.
Add the napa cabbage and bell pepper and cook for 4 minutes, stirring gently. The cabbage should wilt but still keep a little bite, and the pepper should stay bright. This is the moment that makes it taste like a vegetable-forward dinner instead of a snack that happens to contain vegetables.