For the omelette, add all ingredients to a bowl. Whisk together. To get rid of the clumps of chickpea flour, process it in a processor.
For the broccoli stalk pesto, simply process all the ingredients in a small processor. The broccoli stalks may be difficult to break down, so make sure your processor can break it down by adding the broccoli stalks in first. You may need 1-2 tbsp of water to get the pesto to your desired texture.
For the miso mushrooms, kale, and onions, heat 1 tbsp olive oil in a saucepan over medium heat. Add the onions, mushrooms, miso, and garlic powder if using. Break apart the miso as you stir. Once the mushrooms have significantly softened, add the kale and stir it all together until it's done, so about 2-3 minutes.
For the omelette, heat a small 8-to-9-inch pan over medium heat. Grease it with vegan butter (recommended) or olive oil. Add a fourth of the batter (¼ cup to the pan). Flip after about 2 minutes. It should be very easy to flip.
Add some of the pesto and mushroom filling to half the omelette and fold it in half with a spatula. Cook for about 2 minutes before removing it from the heat and repeating for the next omelette.
Serve with some more pesto if you'd like (I like) and some arugula!