How to Make It
Preheat the oven to 325°. In a large enameled cast-iron casserole, heat the olive oil. Season the pork with salt and pepper and cook over moderately high heat, turning, until golden brown all over, about 8 minutes. Add the peaches, yellow tomatoes, gin, rosemary, ginger and 1/2 cup of water and bring to a boil. Cover and braise in the oven until the pork is very tender, about 3 hours. Transfer the pork to a work surface and let cool slightly. When cool enough to handle, shred the meat into large pieces.
Meanwhile, working in 2 batches, puree the braising liquid in a blender until smooth; wipe out the casserole. Strain the sauce through a sieve set over the casserole. Simmer the sauce over moderate heat, stirring occasionally, until slightly thickened, 10 minutes.
In a large pot of salted boiling water, cook the pasta until al dente. Drain, reserving 1/2 cup of the pasta water. Stir the shredded pork, pasta, pasta water, cherry tomatoes and the 1/2 cup of cheese into the sauce and cook until hot, about 3 minutes. Season with salt and pepper. Transfer the pasta to bowls, garnish with basil and pass extra cheese at the table.