Preheat the oven to 325 degrees F.
Line 2 heavy large baking sheets with aluminum foil. Arrange the salami in a single layer over the baking sheets. Bake until the salami slices are amber brown, watching closely to ensure they brown evenly, about 15 minutes. Transfer the salami crisps to a paper towel-lined baking sheet to absorb the excess oil. Set aside to cool.
Spoon a dollop of sour cream on top of each salami crisp. Sprinkle the basil over and serve.
Do-Ahead Tip: The salami crisps can be made 8 hours ahead. Store in airtight containers and keep at room temperature. RECOMMENDED WINE #1: Ferrari Brut Methodo Classico N/V REGION/ORIGIN: Trentino GRAPE/VARIETAL: Chardonnay and Pinot Noir RECOMMENDED WINE #2: La Valentina Montepulciano d'Abuzzo 2002 REGION/ORIGIN: Spoltore, Abruzzo GRAPE/VARIETAL: Montepulciano d'Abruzzo