Preheat the oven to 425 degrees F and position a rack in the upper third of the oven.

Line a sheet pan with aluminum foil or parchment paper. Place the tomatoes on the sheet pan and drizzle with ¼ cup of the olive oil. Season with ¼ teaspoon of the salt and ¼ teaspoon of the pepper. Scatter the thyme sprigs and garlic cloves among the tomatoes and toss everything well to coat. Transfer to the oven and roast until the tomatoes are caramelized on top and have burst and released some of their liquid, usually about 20 minutes. 

Remove the tomatoes from the oven, discard the thyme sprigs and transfer the garlic cloves to a cutting board. Finely chop the garlic (or use the side of your knife to smash it into a smooth paste) and transfer to a large heatproof bowl with the blistered tomatoes. Fold in the salami, balsamic vinegar, remaining 2 tablespoons olive oil, oregano, shallot, cheese, arugula, and remaining ½ teaspoon salt and ¼ teaspoon pepper. 

Bring a large pot of salted water to a boil and cook the pasta according to package direction to al dente. Strain it and immediately, reserving ½ cup pasta water, and add it to the bowl along with the tomatoes and salami. Add the basil and toss quickly to combine. Add the reserved pasta water as needed. Taste and adjust the seasoning if necessary. 

Serve the pasta hot or warm, garnished with additional basil, a sprinkling of black pepper, and a drizzle of extra virgin olive oil if desired.