For the tomato jam: Heat the oil in a pot over medium heat. Add the plum tomatoes, onion, salt and black pepper cook until the tomatoes are very soft and the onions are translucent, 20 to 30 minutes. Add the sugar
, lime zest
and juice, dried peppers, garlic, cumin, cinnamon and allspice
for an additional 60 minutes.
Add the fire-roasted tomatoes to the mixture and puree. Refrigerate overnight.
For the Japanese bbq sauce: Whisk
together the hoisin sauce
, vinegar, honey
and Sriracha in a small bowl.
For the onion strings: Heat the peanut oil
to a temperature of 180 degrees F., using a high-heat thermometer for accuracy.
Whisk together the flour, cornstarch, salt, beer and cayenne if using in a large bowl to make the batter
. In batches, dredge
the onion in the batter, letting the excess drip off.
Cook the onions in the deep fryer in batches. Make sure you dont place too big a batch in the fryer or it will lower the oil temperature. Once the onions
have started to brown a little, remove them from the deep fryer and place them onto a plate lined with a paper towel.
For the burgers: Fry
the eggs sunny side-up on medium heat with a enough butter to keep the eggs from sticking, depending on the size of your pan and the number of eggs
you choose to fry at once.
Cook the beef patties on a char broiler or grill
to the desired temperature. Thirty seconds prior to taking the burgers off the char broiler, lay a piece of cheese on top of each and cover to melt
Lightly toast the buns on the char
broiler. Smear 1 1/2 ounces of the tomato jam on the bottom of each hamburger bun
. Place a burger patty
on top. Add a fried egg and then some of the onion strings. Drizzle
each burger with 1 ounce of the Japanese bbq sauce to finish. Top with the bun tops. Reserve remaining tomato jam and bbq sauce for another use.