Heat butter in a medium frying pan over medium heat and cook the leeks until just soft, but not coloured, 3 to 4 minutes. While the leeks are cooking, grate the potatoes and squeeze out any excess moisture by placing in a clean tea towel and wringing out.
Combine cooked leek, grated potatoes, thyme, egg, olive oil, salt and pepper.
Heat a drizzle of olive oil in a medium frying pan over medium heat (you can use the pan the leeks were cooked in, wipe it clean with paper towels first).
Take ½ cup of rosti mixture and shape into a patty about 1 to 2 cm thick. Repeat with remaining mixture.
Place patties into the hot pan and cook for 3 to 4 minutes on each side until golden brown. Try to avoid moving the rosti for the first minute or two to let a nice crust form. This dish is delicious served with poached eggs and tomato relish for brunch.