Preheat oven to 350°F. Rinse and pat dry the whole cherry tomatoes. Place them in a 9×13 baking dish or oven-safe skillet in a single layer.
Tuck in the garlic cloves, and thyme sprigs among the tomatoes.
Sprinkle salt and pepper over the tomatoes. Pour the extra virgin olive oil over the top until the tomatoes.
Bake covered tightly with foil for 1 hour, or until the tomatoes are soft, blistered, and and the garlic is caramelized.
For best results, allow the confit to cool for 10 minutes, then add the basil leaves to it. Once cooled completely, transfer to a jar or container, making sure the tomatoes are fully covered in oil. Add more olive oil if needed. Store in an airtight container in the fridge for up to 2 weeks.