Add olive oil to a medium pan and bring to medium-high heat.
Add grape tomatoes and sauté for about 90 seconds to 2 minutes, until slightly blistered.
Add shallots, garlic, and tomato paste and sauté for 30 seconds, until tender and fragrant.
Add chardonnay to pan and cook until reduced to 1/4 in volume (almost dry), about 90 seconds.
Add heavy cream and bring to a boil for about 1 minute, then reduce to medium-high heat. With the back of a spoon, crush grape tomatoes, then continue to cook heavy cream until slightly thickened, about 2 minutes.
Whisk in fontina cheese and basil. Cook until cheese fully melts and fondue has a sauce-like consistency.
Season to taste with salt and pepper and keep warm until served.