Slow roasting is an excellent technique for making magic with summer's best cherry tomatoes. Though the dish is supremely simple, you need to build in a good two hours to allow the tomatoes to get tender and nearly caramelized. Feel free to roast the tomatoes and make the garlic/basil oil well ahead of time. Toss them together and leave at room temperature until dinnertime.
Preheat oven to 300 degrees F.
Cover a baking sheet with parchment paper. Put the cherry tomatoes on the baking sheet and toss with 1 tablespoon olive oil and 1/4 teaspoon salt. Cook until the tomatoes get very tender and begin to shrivel, 2 hours. Remove from heat.
Just after putting the tomatoes in the oven, pour the remaining 1/4 cup olive oil into a large bowl. Smash the garlic cloves with the side of a chef's knife, peel, and add to the oil along with the basil. Stir well and set aside while the tomatoes roast.
When the tomatoes are done, transfer them to the bowl with the oil and stir gently.
When you're ready to eat, cook the pasta in a large pot of generously salted water until al dente. Drain well. Add hot pasta to the bowl with the tomatoes, 1 teaspoon kosher salt, and stir to combine. Taste and add more salt if needed. Serve in shallow bowls with freshly grated Parmesan on top.