Preheat oven to 300.
To make the crostinis, place the sliced Ciabatta on a baking pan lined with parchment paper. Bake until crispy, about 15-20 minutes. Allow to cool completely at room temperature. If you are doing this ahead of time, store at room temperature in an airtight container for 2-3 days.
Stack the basil leaves, roll them tight, and slice thin with a sharp knife (chiffonade). Combine with tomatoes, oil, vinegar, salt and pepper in a mixing bowl.
Divide the mixture among the crostinis, about 3-4 Tbsp per crostini. Drizzle with more extra virgin olive oil and balsamic vinegar as desired.