1Preheat the oven to 350?F.
2Grate the potatoes using the coarse side of a box grater onto a clean tea towel or double thickness of paper towel. Sprinkle with salt and pepper, then gather up and squeeze out any excess moisture.
3Meanwhile, set a heavy, ovenproof (cast iron is ideal) 8 or 9-inch skillet over medium-high heat. Add a drizzle of oil and dab of butter. (If you like, sauté your veggies first, then set them aside and wipe out the pan before starting on the potato crust.) Put the grated potatoes into the pan and use the bottom of a metal measuring cup to press the potatoes evenly onto the bottom and up the sides of the pan. Cook for 5-8 minutes, until the potatoes are golden on the bottom.
4Sprinkle the ham or sausage, veggies, thyme and cheese over the crust. In a small bowl, whisk together the eggs and half & half, adding another pinch of salt and pepper, then pour over the fillings. Slide into the oven for 20 minutes, or until golden. Cut into wedges to serve.