Pour the oil in a 15 ½” x 10” baking pan. Place both packs of dough in the pan and turn them over to cover it in the oil, then press and spread it out until it fits the entire pan. Cover the pan and place it in a warm spot to rise for an hour.
Heat a large skillet over medium-high heat and add the butter. Stir the onions, cooking for 10 minutes until softened. Stir in the balsamic vinegar. Cook for another 10-15 minutes until caramelized.
Preheat the oven to 425°F. Uncover the pan with the dough and cover it with onions and strawberries. Sprinkle with flaky salt. Drizzle with olive oil. Bake for 15-20 minutes until it’s golden and toasty. Remove from oven and let cool. Top with fresh basil and cut into pieces.