Preheat oven to 300°F. Whisk together olive oil, balsamic vinegar, and honey in a medium bowl until emulsified. Add strawberries to bowl, toss to coat with dressing, and let marinate 15 minutes.
Meanwhile, spread pine nuts on a rimmed baking sheet and toast in oven until lightly browned, about 15 minutes, shaking pan occasionally so nuts toast evenly. Let nuts cool before using.
Toss arugula and basil together and strew across a platter. Place burrata in center, and gently break open at top, to expose cream and mozzarella inside. Spoon macerated strawberries and dressing over arugula. Scatter pine nuts on top, season with salt and pepper, and serve with crostini.
