Prepare the Potatoes (Can be done in advance):
Preheat your oven to 400°F. Scrub the potatoes clean, pat dry, and prick several times with a fork.
Place directly on the oven rack and bake until completely tender when pierced with a knife, about 45-60 minutes depending on size.
Remove from oven and let cool completely. This can be done up to 24 hours in advance.
Make the Gnocchi:
Once potatoes are cool enough to handle, peel away the skins and pass the flesh through a potato ricer or food mill into a large bowl. If you don't have either tool, mash very thoroughly until no lumps remain.
Spread the riced potatoes on a clean work surface and allow to cool completely. This step is crucial - warm potatoes will absorb too much flour and create heavy gnocchi.
Once cool, form a well in the center of the potatoes. Add the beaten eggs and sprinkle with salt.
Begin gradually incorporating the flour, starting from the center and working outward. Knead gently until a soft, slightly sticky dough forms. Avoid overworking the dough, which can make the gnocchi tough.
Divide the dough into 6 equal portions. On a lightly floured surface, roll each portion into a rope about ½-inch thick.
Cut each rope into ¾-inch pieces. If desired, roll each piece against the tines of a fork to create traditional ridges (these help the sauce cling better).
Place finished gnocchi on a lightly floured baking sheet. Cook immediately or refrigerate for up to 4 hours.
Prepare the Sauce:
In a large, heavy-bottomed skillet over medium heat, add a tablespoon of olive oil.
Add diced onion and cook until translucent, about 5 minutes.
Add minced garlic and cook for another minute until fragrant.
Add chopped tomatoes and cook until they begin to break down, about 10 minutes.
Pour in bone broth and simmer for 15 minutes, allowing the sauce to reduce slightly.
Stir in heavy cream and simmer for another 5 minutes.
Meanwhile, bring a large pot of generously salted water to a rolling boil.
Cook the Gnocchi:
Gently drop about half the gnocchi into the boiling water. They'll sink at first, then rise to the surface when cooked (about 2-3 minutes).
Remove with a slotted spoon and transfer directly to the sauce. Repeat with remaining gnocchi.
Gently toss the gnocchi in the sauce, adding a splash of pasta water if needed to loosen.
Stir in the crumbled bacon, grated Parmesan, and Asiago. Season with salt and pepper to taste.
Remove from heat and scatter with torn basil leaves just before serving.
Serve in warmed bowls with additional grated cheese on the side. This dish pairs beautifully with a simple arugula salad dressed with lemon and olive oil.