Cut the cauliflower into florets and pulse them in a food processor until they resemble rice grains. Be careful not to over-process them. Alternatively, you can use pre-packaged cauliflower rice.
Heat the sesame oil in a large skillet or wok over medium heat. Add the minced garlic and diced onion, and sauté for 2-3 minutes until they become fragrant and lightly browned.
Add the diced carrot, bell pepper, and broccoli to the skillet. Stir-fry for about 5 minutes until the vegetables are slightly tender but still crisp.
Push the vegetables to one side of the skillet and add the cauliflower rice to the other side. Cook for 3-4 minutes, stirring occasionally until the cauliflower is tender but not mushy.
In a small bowl, mix the soy sauce (or tamari) and rice vinegar (or lime juice) if desired. Pour the sauce over the stir-fry and stir well to evenly coat the vegetables and cauliflower rice. Cook for an additional 1-2 minutes.
Remove from heat and garnish with sliced green onions and sesame seeds if desired.