Preheat the oven to 400 degrees. Line 2 baking sheets with parchment.
In a large bowl, toss together 1 cup of the pecorino, the panko, and the parsley. Drizzle with ⅓ cup of the oil and toss well. Add the tomatoes, garlic, 1 tsp salt and a pinch of peperoncino. Toss well to coat the tomatoes in the crumb mixture.
Scatter the tomatoes on the baking sheets, scraping any excess crumbs from the bowl on top of them. Bake until the tomatoes are shriveled but still juicy and the crumbs are crisp and golden, 25 to 30 minutes, tossing once halfway through.
When the tomatoes are almost done, bring a large pot of salted water to a boil for the pasta. Add the spaghetti to the boiling water and cook until it is al dente.
Transfer the hot cooked tomatoes to a large serving bowl. Drain the pasta with tongs, and add it directly to the bowl with the remaining ¼ cup pecorino and the basil. Drizzle with the remaining 2 tbsp olive oil, and add a ladle or two of pasta water. Toss well, adding a little more pasta water if it still seems dry.