I freeze my hamburger meat in smaller pieces than that - squares a little smaller than the palm of my hand. I don't get worked up about them all being the same size either - I can grab two large ones or three smaller ones and come up with the amount of ground beef I want.
For spaghetti sauce, shepherd's (technically cottage) pie etc, I defrost the right number of squares in the microwave (on a plate or in a wide shallow bowl) then into the hot pan. Usually the centre is still frozen but it doesn't matter, it will defrost while the rest is browning. Sometimes a corner starts to cook but again this is not a big deal. For hamburger patties, I buy medium instead of lean or extra lean, and form them into patties before freezing. This means I know at a glance which is which in the freezer, and I don't have to worry about the meat partly cooking in the microwave before I form it into patties.
About the only meal this doesn't work for is meatloaf, which really needs ground beef that isn't a teeny bit cooked in one corner already and isn't still frozen in the middle either. I make that only with fresh ground beef which eliminates the problem.