Heat oven to 400ºF. Spray a 9-inch glass pie plate with oil.
Peel and shred the potatoes; wrap them in a paper towel and squeeze out any excess moisture. Add the shredded potatoes to a large bowl and mix in 1 teaspoon olive oil, dill, and garlic; season with salt and pepper. Press into the prepared pie plate, working the potatoes up the sides like a crust. Bake until the potatoes look dry and the edges are golden brown, about 20 minutes. Let cool. Reduce heat to 325ºF.
Heat the remaining olive oil in a large skillet. Add the onion and cook until softened, about 5 minutes. Add the mushrooms and cook another 5 minutes, until soft.
Spread the mushroom and onion mixture into the bottom of the potato crust. Top with the salami and 3/4 of the cheese. In a small bowl, beat together the eggs, milk, and capers. Pour into the crust, shaking the pan gently if needed to let the egg settle. Top with the remaining cheese and sprinkle with black pepper.
Return the quiche to the oven and bake for 20-30 minutes, or until the center is set. Let cool before slicing.