Preheat the oven to 150° and position a rack in the center. Spread the olives on a baking sheet and transfer to the oven. Bake overnight, until the olives are dry. (Alternatively, you can also do this in a food dehydrator if you have one.)
Put the olives into the bowl of a food processor and pulse until finely ground. With the machine running, pour in the olive oil and Tabasco and mix until emulsified.
The black olive musto oil can be made up to 1 week in advance and kept tightly covered in the refrigerator. Stir before using.