Whisk water with soy sauce, nutritional yeast, mustard, vinegar and spices.
Pour half into a skillet and bring to boil. Add broccoli and cook over high heat for a few minutes until the broccoli turns bright green and sauce has reduced. Whisk arrowroot powder into remaining broth until well combined and pour over broccoli.
Add bell peppers and continue to cook over high heat until the broccoli is dark green, the bell peppers are tender but crisp and the sauce has reduced to half.
Spoon this over brown rice to serve and drizzle with remaining sauce.