Combine ground round, salt and pepper and form into thin patties (about 6), cover and refrigerate.
Heat olive oil over medium heat and add onions; sprinkle with salt and sugar. Using tongs, toss onions to coat. Reduce heat to medium-low and cook until caramelized; remove from heat.
Increase heat to medium-high and add burgers, a few at a time, cooking until done.
Combine the Greek yogurt, cucumber, dill, lemon and salt to make Tzaziki sauce.
Combine Feta cheese, olives, jalapeno and olives oil with a fork; mashing together.
To assemble burgers, spread hummus on the bottom half of a bun, add a burger, top with feta mixture, top with another bun bottom and spread Tzaziki on top, then add tomatoes followed by another burger, more feta mixture, caramelized onions and more Tzaziki.