Peel the onions and cut them into thick slices, about ½-inch thick.
Brush the onions on both sides with olive oil. Sprinkle them with salt.
Place the onion slices on the grill (you can place them directly on the grill or on a vegetable grilling rack if you have one).Grill the onions, covered, for 4 to 5 minutes until they get nice grill marks on the bottom and begin to soften, then flip them and grill for another 4 minutes or so. You should feel free to move them about the grill to cooler spots if they look like they are browning too quickly, before they become tender. You can grill them for longer, if you want softer onions, just make sure to flip them as needed and not let the heat get too high – you want them lightly browned and caramelized, not too dark or crispy.
Remove from the grill and serve warm or at room temperature.