Preheat oven to 250F. Plug in waffle maker.
In a large skillet over medium-high heat, add oil. Brown burger about 5-6 minutes, add chopped onion and cook another 3-4 minutes. Once browned, add Worcestershire sauce, beef bouillon, garlic clove, salt and pepper. Turn heat off and let cool a bit.
While burger mixture is cooling, mix together waffle mix, milk, egg, and the second tablespoon EVOO. Add cooled burger mixture and half cup of Provolone cheese.
Brush the hot waffle maker with melted butter, spoon about cup of batter into center of each waffle. Close lid and cook until the waffles are golden brown and release from the waffle griddle cleanly.
Place the finished waffles onto a baking sheet lined with a cooling rack and place them in the warm oven while you finish cooking the rest of your waffles.
While the waffles are cooking, melt butter for the cheese sauce in a small sauce pan over meduim-high heat. Add garlic and cook for a minute. Add flour and cook 1 minute. Add milk and whisk until it comes to a boil and starts to thicken. Add liquid smoke, and cheese; continually stir until cheese is completely melted. Add salt and pepper as desired.
Now plate your waffle and pour cheese sauce over it and enjoy!