For the pasta: Preheat oven to 425 degrees F. Line a baking sheet with parchment paper. In a medium bowl, add the tomatoes, olive oil, salt and pepper, tossing until well combined. Pour the tomatoes onto the baking sheet and roast in the oven for 15 to 25 minutes, or until the tomatoes are nicely browned and caramelized. (Some will be darker than others, don’t let that worry you.) Remove the sheet from the oven and set aside to cool.
Meanwhile, prepare the pesto – see recipe below. (You may substitute 1 cup already prepared, store-bought pesto.)
Bring a large pot of water to a boil. Once boiling add 2 tablespoons sea salt and the pasta, stirring the pasta to prevent it from sticking together. Follow the package directions and cook the pasta until al dente –tender, but firm to the tooth. Drain the pasta well, but do not rinse.
Place the hot pasta in a large bowl, add 3/4 cup pesto (more to taste), mix until combined. Add the roasted tomatoes, and their cooking juices, gently stirring until well mixed. Serve immediately, while warm, with a drizzle of extra virgin olive oil and grated parmigiano-reggiano.
For the pesto: In a food processor, add the garlic, half of the salt and one cup of the basil. Pulse until the basil is chopped, 10 to 12 pulses. Add the rest of the salt and the remaining basil. Pulse again until well chopped, 10 to 12 pulses. Next add the cheeses, pulsing until well combined. Add the pine nuts and pulse until chopped and well combined. Now, with the food processor running, drizzle in the olive oil until the mixture is a loose paste. (Be careful not to process the basil too much, the basil will react to the heat of the food processor and become discolored.) Taste for salt and adjust as needed.