Prepare Sauce: Preheat the oven broiler to high. Place the sliced tomatillos, sliced onion, and garlic on a foil-lined half sheet pan. Toss with the olive oil and season with salt and pepper. Roastunder the broiler for 10 to 15 minutes, tossing several times, until the tomatillos and onions are evenly charred and the tomatillos are very soft.
Remove and allow to cool slightly before processing in a blender. Depending on your preference, you can either choose to make the sauce slightly chunkier or puree it until it is very smooth. Set the sauce aside to cool at room temperature. Add the lime juice and season with additional salt and pepper if needed.
Prepare Salad: Cut the avocado in half, pit, and remove the peel. Cut the avocado halves into ½-inch thick slices. Toss the pieces lightly with lime juice (to prevent oxidation). Brush the avocado slices with a small amount of oil (so they do not stick to the grill). Using a grill pan, grill the avocado slices over high heat for roughly 1 minute on each side. Set aside.
Meanwhile, trim and discard the top, soft leaves of the romaine hearts or reserve for another use. Slice the romaine hearts in half lengthwise. Brush the cut-sides with olive oil and season with salt and pepper. Using an outdoor grill (preferably) or a grill pan over very high heat, grill the romaine hearts until browned on both sides. Depending on the heat of your grill or grill pan, this will take approximately 2 to 3 minutes per side.
Assemble and Serve: For each serving, spoon roasted tomatillo sauce onto a serving plate and swoosh using the back of a spoon. Place one grilled romaine half on top of the sauce, and then top it with 2 to 3 grilled avocado slices, a sprinkle of sliced green onions, and a hefty dose of finely grated cotija cheese. Serve immediately.