In a saucepan or skillet, warm ⅓ cup olive oil over medium-low heat. Add garlic, parsley, and red pepper flakes. Cook, stirring often, for 4 to 5 minutes or until garlic has softened. Set aside to cool.
Roll out two circles of dough. Coat deep-dish pizza pans with remaining olive oil and sprinkle with cornmeal. Place dough circles in the pans and press dough up the sides.
Divide garlic-olive oil mixture over the two pizzas and spread over the bottom of the crust.
Spread 1½ cups of halved grape tomatoes over each crust, followed by ½ cup of pine nuts. Divide Brie between the two pizzas and distribute evenly over the crusts. Sprinkle fresh basil leaves and ½ cup of Gruyère cheese over each pizza.
Preheat oven to 400°F. Bake pizzas until crust is light brown and cheese is melted and bubbly, about 15 minutes.
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