Place the bulgur wheat and 1 cup water in a small pot. Bring the mixture to a boil. Reduce the heat to low, cover, and simmer the bulgur for 12 minutes, or until the water has been absorbed. Remove the pot from heat, fluff the bulgur with a fork, re-cover, and set the bulgur aside.
Cut the broccoli into florets and pieces. Place them into a food processor fitted with the S blade. Pulse until the broccoli is in small (about pea-sized) pieces. Alternatively, you can finely chop the broccoli by hand.
Heat a skillet or deep frying pan over medium heat. Add a few tablespoons of water to the hot skillet. Add the finely chopped broccoli and cover the skillet or pan. Allow the broccoli to steam cook for about a minute, then remove the cover and continue cooking, stirring the whole time, for another 1-2 minutes. The broccoli should turn bright green and no longer taste raw, but it should retain a lot of its crunch. Remove the skillet with the broccoli from heat.
Wipe down the food processor and then add the parsley and mint. Pulse the herbs until they're finely chopped.
Place the cooked bulgur, broccoli, herbs, and finely chopped onion into a mixing bowl. Add the olive oil, lemon, salt, and garlic. Mix everything well. Taste and add additional salt as desired. If you like, top the tabbouleh with pomegranate arils. Serve.