Heat cream and espresso in a small pot until bubbles form; let cool for 10 minutes.
Place 2 cups white chocolate chips in a large bowl. Strain the cream into the bowl over the chips. Set the bowl over a pot of simmering water, stir until chocolate is nearly melted, then remove from heat.
Add mascarpone and salt, whisk until combined. Refrigerate until firm, at least 2 hours.
Roll ganache into 24 (1-inch) balls; freeze until solid.
Microwave 1 tablespoon oil and remaining 1 cup white chocolate chips until melted. Dip 8 balls, then shave dark chocolate on top.
Microwave semisweet chips and remaining oil, dip 8 more balls, sprinkle with ladyfingers.
Roll remaining 8 balls in cocoa powder. Refrigerate until firm. Enjoy your tasty truffles!