Sauté onions in the butter until lightly caramelized. Add garlic and sauté until fragrant, 30 seconds to a minute.
Set aside and let onion and garlic mixture cool slightly.
In a large mixing bowl, add in remaining ingredients except for the feta.
Add onions and garlic to the bowl. I find that using your hands to combine the ingredients works the best, but a large spoon will do the trick as well.
Once everything is evenly combined (donʼt over mix, you loose the burger texture), add the feta and mix until evenly distributed.
Divide meat into 6 even portions and grill to your preferred level of doneness.