Heat a medium-sized non-stick pan or cast iron skillet over medium heat. Add the pancetta and sauté until lightly browned, about 7 minutes. Strain the pancetta from the pan, reserving the rendered fat, and set both aside until ready to use.
Place your minced onions in a large bowl. Peel your potatoes and coarsely grate them using the large holes on a box grater. Mix the potatoes with the onions.
Now for the most important step: Remove as much moisture from the potato and onion mixture as you can, which you can do in two ways. Option 1: Wrap the mixture in a clean dish towel and then twist the towel as tightly as you can to wring as much water out of the potatoes as humanly possible. (Obviously, you should do this over the sink. Duh.) Option 2: Take handfuls of the potato mixture and squeeze them to release as much water as you can, transferring the dry potatoes to a new bowl as you go. Either option will work well, but do not skip forget this step, people.
Mix the cooked pancetta into the potatoes mixture and season with salt (about a teaspoon) and fresh ground pepper.
Heat a tablespoon of the rendered fat from the pancetta and a tablespoon of olive oil until smoking slightly. (To check if the oil is hot enough, add a strand of potato to the pan. If it sizzles enthusiastically, the oil is ready.) Carefully add half of the potato mixture to the pan in an even layer and top with the diced mozzarella. Add the remaining potato mixture and pat it down with a spatula.
Cook for 2-3 minutes and then lower the heat slightly. You still want to hear the potatoes lightly sizzling, but you don’t want them to be burning. Cook the rosti for 12-15 more minutes until the underside is nicely browned and the potatoes become tender.
Flip your rosti. To do this, place a plate over the pan and carefully flip the rosti onto the plate.
Heat another tablespoon of rendered fat from the pancetta and a tablespoon of olive oil. When hot, slide the rosti from the plate back into the pan. Cook for another 10-12 minutes until the underside is browned and the center is tender (which you can test with the tip of a sharp knife.) Remove the rosti from the pan and allow it to cool slightly.
While the rosti is cooking. Slice your tomatoes in half with a serrated knife and place them in a small bowl. Toss with 1 teaspoon of olive oil and season with salt and fresh ground pepper.
Slice your rosti, and top with arugula and tomatoes. Serve immediately. Potatoes were a good choice.