1. Heat oven to 400 degrees. Wrap garlic in aluminum foil and bake until golden brown and tender, about 45 minutes. Remove from oven, open foil, and set aside until cool enough to handle.

2. Slice off about 1/4 inch of the pointed end of the garlic head and squeeze the roasted garlic into a large, nonreactive bowl. Add remaining ingredients, except pasta and goat cheese, and mix to combine. Cover and let stand at room temperature, stirring occasionally, for at least 2 hours and up to 6 hours.

3. Bring a large pot of cold salted water to a boil. Add the orecchiette and cook until al dente, about 12 minutes. Drain pasta well and combine with the tomato sauce. Add the goat cheese, if desired, and toss to combine. Transfer to a large serving dish, garnish with more chopped basil, and serve immediately.