Preheat oven to 450°F. In a medium saucepan, combine the mung beans with 2 cups water, season with salt, and bring to a boil over high heat. Cook covered until almost all of the water is absorbed, about 20 to 25 minutes — the mung beans will still have a good bite.
Rinse, deseed, and roughly chop the red pepper. Rinse and destem the basil. To a food processor, add the chopped pepper, basil, garlic, nutritional yeast, sesame seeds, hemp seeds, and a pinch of salt and pepper. Pulse to combine and add 2 tbsp olive oil. Blend pesto on high until fairly smooth, and season to taste. Scrape the pesto into a bowl and then wipe your food processor clean.
Add the mung beans to your food processor. Pulse a few times to break them up, then add the chickpea flour, flaxseed meal, and ½ cup water. Season with salt and pepper. Run on high until well blended, scraping the sides down as needed. The final dough should be fairly stiff.
Line a baking sheet with parchment paper. Divide the dough in half and shape each half into a ball. Place the two dough balls on the lined baking sheet and gently press down until the crusts are about ¼-inch thick. Place in the oven and bake until the edges are lightly browned, about 10 to 15 minutes.
Rinse and dry the broccoli and peel the shallot. Thinly slice both. Place a medium skillet over medium-high heat and add 1 tsp olive oil. Add the sliced vegetables and 2 tbsp water, and cook until the shallots are translucent and broccoli is tender, about 4 to 5 minutes. Add the pesto to the pan to warm it through. Season to taste with salt and pepper.
Once the mung bean crusts come out of the oven, top each with the broccoli pesto. Carefully cut the pizza into slices. Rinse and dry the arugula and toss with 1 tsp olive oil and a pinch of salt and pepper. Serve your pizza with some of the arugula on top with the remainder as a side salad. Mangia!