Preheat the grill on high and close the lid. Set all burners to direct heat.
Trim the top 2-3 inches (the flimsy leafy grean part) off of the romaine lettuce and keep it for a side salad. Don't throw it away!! Set that aside.
Generously season the broccoli and romaine with olive oil, salt, pepper and any extra lime juice (if preferred.) Make sure to get olive oil in all the nooks and crannies in the romaine! Drizzle olive oil on the bread and season with salt and pepper.
Once the grill hits 500-600 degrees Fahrenhet, grill the broccoli for 7 minutes with the lid closed. Flip, then grill for another 3-4 minutes. If needed, remove any smaller pieces that cook more quickly than the larger ones.
Remove the broccoli and place on a plate. Cover the broccoli with foil to keep it warm. Add the romaine flat side down to the grill. Close the grill and cook the romaine for 2 minutes, then flip it. Add the lime slices (flat side down) and the bread, then grill with lid closed for 2 minutes. Remove the lettuce and plate, then return to the grill to flip the bread. Grill the bread on the other side with the lid closed for another 2 minutes, then remove the lime and bread and plate everything. Enjoy ASAP with generous amounts of tahini Caesar!