To prep the potatoes: peel them, then grate using a box grater or food processing grating blade. Place grated potatoes in a towel, then wring it out a few times to squeeze out excess liquid. Put potatoes in a large bowl.

On low heat, melt the butter in a heavy saute pan. Pour the butter over the grated potatoes, season with salt and pepper to taste, and toss together well.

Form potato mixture into 6 patties.

Heat vegetable oil in the saute pan over medium heat.

Place 3 potato patties in the pan, then flatten them out a bit by pressing down with a spatula. Cook until brown one the bottom, then flip over. Place half of the arugula and goat cheese on top of each potato pancake, then place the remaining potato patties on top. Pat down to flatten again. Cook for 10-12 minutes or until bottoms are lightly browned.

Using a large spatula, carefully flip over each potato pancake. Top with the remaining arugula and goat cheese, and cook for another 10-12 minutes.

Transfer the rosti potatoes to a large plate, and serve while they're still hot.