Preheat the oven to 375 degrees.
Place the strawberries on a rimmed baking sheet, then add the balsamic vinegar, honey, and salt and pepper. Toss until evenly coated. Bake for about 20 minutes, turning half way through, or until dark and soft, then remove from the oven and toss again. Depending on strawberry size, you may need to roast longer—mine were huge, so I gave them more time (see this tutorial for more tips).
Set the oven to broil.
On a separate baking sheet, lay out the baguette slices and drizzle with olive oil and season with salt and pepper on both sides. Broil until golden brown, 1 to 2 minutes per side.
Place the burrata balls in a small serving bowl and cut an “X” shape on the top of each ball. Drizzle generously with olive oil and balsamic, if using, and season with salt and pepper. Spoon the roasted strawberries into the bowl around the burrata, then top with basil leaves.
Serve family-style with the prepared crostini on the side, and enjoy!