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Step 1
Put 4 tablespoons of the olive oil and the chopped bacon in the big skillet and set over medium-high heat. Stir and cook for 3 or 4 minutes, to render bacon fat. Stir in the chopped onion, and cook until it is sizzling and wilting, about 3 minutes. Spill in the cubed potatoes, toss well in the fat, then spread them in the pan. Season with the salt, and cook, tossing and turning the potatoes frequently, for another 3 or 4 minutes, until the cubes are lightly crisped all over.
Step 2
Pour in 4 cups water, stir everything around, and scrape up any crust on the skillet bottom. Bring the water to a gently bubbling boil and cook, stirring frequently, for about 20 minutes, until the potatoes are cooked. The soup (or sauce, depending on your point of view) should reduce so it barely covers the potato cubes.
Step 3
Meanwhile, bring 6 quarts of salted water to the boil in a pasta pot. After the potatoes have cooked for about 10 minutes, drop the ditalini into the pot and cook al dente. Drain the ditalini, and stir into the thickened potato soup/sauce. Stir in the remaining 2 tablespoons olive oil, and simmer the pasta e patate together for another 3 minutes or so, to an even denser consistency.
Step 4
Stir in the diced tomatoes, cook for a minute, and adjust salt to taste. Turn off the heat, scatter the cubed provola all over, and stir into the pasta e patate continuously as it melts into threads. Finally, stir in the grated cheese. Serve immediately, in warm bowls.