Sauté the onion in olive oil until soft and lightly browned around the edges in a large skillet or griddle. This took about 10 minutes. Lift the onions out into a bowl and set aside.
In a medium bowl, beat together the eggs, milk, thyme, and spices. Dip the bread in the egg mixture. Brown each slice on both sides in the same pan you cooked the onions in, adding more oil if needed.
Top each slice with 2 slices of Canadian bacon, onions, and shredded cheese. Cover, reduce heat to low, and cook until the cheese melts, about 5 minutes.