In a 10-12" nonstick frying pan, combine onion, garlic, and
half the broth. Bring to a boil over high heat; stir often until
liquid evaporates and browned bit stick in pan.
Add half the remaining broth; stir to scrape browned bits
free, then boil again until liquid evaporates and browned bits
form. Repeat step with remaining broth, cooking until liquid
evaporates. Set onion mixture aside.
In a bowl, mix together tuna, celery, and mayonnaise. Top 4
slices bread equally with tuna mixture, onion mixture, cheese,
and remaining bread
Wipe the pan clean. Place over medium heat and add 2
sandwiches. (If you have another nonstick frying pan, toast all
the sandwiches at once.) Cook until sandwiches are toasted on
the bottom, about 4 minutes. Turn over and toast tops, about 4
minutes more.