Place ladyfingers into the bowl of a food processor and pulse until finely ground.

Add powdered sugar, espresso powder, and salt to the ground ladyfingers and pulse several times until combined.

Add mascarpone, coffee liqueur, and vanilla to the mixture and pulse until thoroughly combined and comes together in a thick dough.

Line a baking sheet with parchment paper. Scoop out 1 tablespoon dough and roll it into a ball. Place on the baking sheet. Repeat with remaining dough.

Place the pan into the freezer until dough balls are chilled through, about 1 hour.

Place white chocolate chips and vegetable oil into a microwave-safe bowl. Heat at 50% power in 30-second intervals, stirring after each interval, until melted, about 1 to 1 1/2 minutes.

Remove dough balls from the freezer. Carefully dip a dough ball into melted white chocolate until thoroughly coated. Allow some excess chocolate to drip off; then carefully place it back onto the lined baking sheet. Repeat this process with remaining truffles.

Place truffles into the refrigerator until chocolate is set, about 10 minutes.

Dust truffles with cocoa powder just before serving.