Pasta with No-Cook Tomato Sauce

Ingredients (10)

• 1 pound cherry or grape tomatoes, halved or quartered if large
• 1/4 cup olive oil
• 2 medium garlic cloves, minced
• 2 tablespoons finely chopped Italian parsley leaves
• 1 tablespoon finely chopped oregano leaves
• 1 teaspoon kosher salt, plus more as needed
• 1/2 teaspoon freshly ground black pepper
• 1 pound dried short pasta, such as penne, gemelli, or fusilli
• 5 ounces chèvre (fresh goat cheese; about 3/4 cup), at room temperature
• 1/4 cup freshly grated Parmesan cheese (about 1 ounce), plus more for serving