Boil the pasta: Cook the pasta in salted boiling water until just al dente, about 9 to 11 minutes. Reserve 1 cup of the starchy pasta water before draining.
Sauté the garlic: Heat olive oil in a large skillet over medium heat. Add the minced garlic and cook until fragrant, about 30 seconds, stirring so it doesn't burn.
Add the broth: Pour in the chicken broth and let it warm through for about a minute, scraping up any browned bits from the pan.
Melt the Boursin: Crumble the Boursin cheese into the pan along with 1/2 cup of the reserved pasta water. Stir over low heat until the cheese melts into a smooth, pale sauce.
Combine with pasta: Add the drained pasta and cherry tomatoes to the skillet, tossing until everything is evenly coated and the tomatoes just start to soften.
Adjust the sauce: Add more reserved pasta water, a tablespoon at a time, until the sauce coats the pasta loosely and clings to a spoon without feeling thick.
Season to taste: Taste the pasta and add salt and black pepper as needed, keeping in mind the Boursin is already seasoned.
Finish and serve: Top with grated Parmesan and chopped parsley or basil. Serve immediately while the sauce is still silky and warm.