Heat oil in a large skillet over medium heat. Once hot, add the onion to the skillet and sauté for 1 minute. Next, add the garlic. Sauté until onions are soft.
Stir the broccoli in with the onion and garlic. Sauté for 1 1/2 minutes, stirring the skillet once or twice to prevent burning.
Add the kale and vegetable broth to the skillet. Stir, cover, and turn heat down to medium-low for 1 minute.
Remove lid, stir in 2 Tablespoons nutritional yeast, the sea salt, and the black pepper. Turn heat back to up to medium and sauté, stirring occasionally, until liquid is absorbed and broccoli "rice" is tender.
Taste, add more seasonings if desired. Sprinkle each serving with additional nutritional yeast (optional).