Grate the rutabaga on the coarse side of a box grater. Then grate the onion, transfer the grated veg onto a tea towel and squeeze well. Discard the liquid and transfer the grated vegetables to a mixing bowl.
Add the salt, parmesan cheese, and potato starch to the grated vegetables and toss the mixture together with your fingertips to combine. The mixture should be quite dry and fluffy.
Heat the olive oil in a non-stick skillet over medium-high heat. Pack the mixture into patties and add to the pan. I like to use a portion scoop for this, and I pack the mixture quite firmly into the scoop before shaping them into patties. The mixture will make 8-10 golf ball-sized patties. You can also make them larger if you prefer.
Fry the patties for 6-7 minutes on the first side, then flip and fry for an additional 4-5 minutes on the other side. Keep an eye on them as they get pretty dark quite quickly.
Serve with sour cream or whatever you would normally serve with latkes.