Combine all ingredients in a bowl and mix thoroughly with your hands for several minutes. Divide the mixture, and take the first half. Roll it into a (tennis sized) ball for a good minute or two. Then place in one hand and start "clapping" it from one hand to the other until you essentially have a large patty (about 6 inches in diameter). Repeat with the second.
Cover a cutting board with plastic wrap to prevent stickiness, and place your patties down. Shape more with your fingers if necessary. Pljeskavice should be smooth and evenly thick everywhere.
Fire up the grill. When it's deliriously hot, throw on your pljeskavice. Grill for two minutes on the first side, then flip and grill another 2 minutes. At this point, flip to the first side again and repeat the process, this time leaving the pljeskavice on for about 2-3 minutes on each side.
Two-three minutes before the end of grilling, cut the hamburger buns in half and place over the patties so they soak up the moisture.
Garnish pljeskavice with whichever hamburger sides you prefer.
You are also welcome to follow your own timing and preferences regarding meat wellness. Recommendations above are for medium to well done meat. Traditional pljeskavice sides include yellow onion, tomato, cheese spread and pepper spread.