Preheat a griddle to 350F.
Combine the mayonnaise and vinegar in a small bowl. Spread 1 tablespoon on each cut side of the focaccia.
Add a little oil to the griddle. Place the focaccia, mayonnaise side up, on the griddle. Put 2 slices of cheese on top of each piece of bread, and cover with a heatproof bowl to melt the cheese.
Meanwhile, divide the turkey into 2 portions and put on the griddle to warm. Place the bacon slices in an X over each portion, and cover with the avocado and remaining cheese. Once the cheese is melted all around, put a mound of turkey on 2 bottom halves, and top with the remaining bread.
Add a bit more oil to the griddle and press the sandwiches with a cast-iron pan or other heavy thing, turning once, until the bread is crisp on both sides.