1 package (17.3 ounces/2 sheets) puff pastry, defrosted
Good olive oil
4 cups thinly sliced yellow onions (2 large onions)
3 large garlic cloves, cut into thin slivers
Kosher salt and freshly ground black pepper
3 tablespoons dry white wine
2 teaspoons minced fresh thyme leaves
4 tablespoons freshly grated Parmesan, plus 2 ounces shaved with a vegetable peeler
4 ounces garlic-and-herb goat cheese (recommended: Montrachet)
1 large tomato, cut into 4 (1/4-inch-thick) slices
3 tablespoons julienned basil leaves