Preheat the oven to 375°F (190°C).
Place the grape tomatoes and minced garlic in a large 9×13-inch baking dish; drizzle with the olive oil and toss to coat.
Set the package of Boursin cheese in the center of the dish among the tomatoes and bake for 10 minutes, until the cheese softens and tomatoes begin to blister.
Remove the dish from the oven and stir in the dry orzo, chicken (or vegetable) broth, heavy cream, and salt, breaking up the softened Boursin and crushing the tomatoes as you stir to combine.
Return the dish to the oven and bake for 30 minutes. After 30 minutes, remove and stir; test the orzo for doneness and return to the oven up to 10 more minutes if needed.
When the orzo is tender and the mixture is creamy, remove from the oven, stir once more, and sprinkle with chopped basil before serving immediately.