Prepare a medium-hot grill.
In a large bowl, microplane 1 clove of garlc.
Add 4 tbsp neutral oil to the garlic and stir together well.
Remove any dead leaves from the outside of the romaine, Cut the heads in half and if necessary, wash the lettuce by submerging it in cold water and agitating it. Dry the lettuce as much as possible, add it to the bowl and use clean hands to completely coat the lettuce in the garlic and neutral oil mixture. Season the lettuce well with salt and pepper, particularly the cut side.
Place the lettuce cut side down on the medium-hot part of the grill. The lettuce should start to sear when it hits the grill grates, if not, the grill needs to be a little hotter. Cook the lettuce for about 2-3 minutes or until you the lettuce has some nice char and the leaves are just begining to wilt.
Flip the lettuce and cook on the other side for another 1-2 minutes. The lettuce is done cooking when the leaves have softened and wilted but the center core still retains a bit of structure. If necessary, you can press on the romaine as it cooks.
Place the grilled romaine on a plate and drizzle with all of the bagna cauda. Top with as much crispy breadcrumb as you like and a few lemon wedges if you prefer.