Preheat the broiler to high.
Heat a deep pot over medium to medium-high heat. Add EVOO, once around the pan, and butter to the pot. Add the onions to the pot as you slice them and then the chopped garlic. Season with salt and pepper. Add rosemary sprigs and a bay leaf.
Cook the onions for 20-25 minutes, stirring frequently, until tender, sweet and deep caramel-colored. If the onions are burning in spots before browning all over, add a splash of water and stir every now and then, scraping the bottom of the pot.
While the onions are cooking, make the grape tomato topping: In a small bowl, combine the grape tomatoes, basil, a little salt and pepper.