Cover baking sheet with waxed paper. Place 18 of the cookies on the baking sheet.
With small ice-cream scoop (about 2 tablespoons), place 1 scoop ice cream on 1 cookie. Top with second cookie. Repeat with remaining cookies and ice cream to form 18 sandwiches. Work as quickly as possible to keep ice cream from melting; you may want to freeze first sandwiches while working with the remaining cookies and ice cream.
Freeze assembled sandwiches overnight to soften cookies.
To make dipping mixture for cookies, place white chocolate in small microwave-safe glass bowl. Melt the chocolate on 100 percent power for 1 minute. Stir chocolate until smooth. Stir in the oil. Microwave for 30 seconds if necessary to heat through; stir until the mixture is smooth. Let stand at room temperature until cooled slightly, about 15 minutes; the temperature of the chocolate should register about 85 degrees F on instant-read thermometer.
Stir the ground cloves into the melted chocolate. Working quickly, dip half a sandwich cookie into chocolate; scrape any excess chocolate off the cookie back into the bowl. Return the dipped sandwich to the waxed paper-lined baking sheet. Repeat with the remaining sandwiches. Return the baking sheet to the freezer. Freeze until chocolate is set, about 1 hour.
Transfer sandwiches to medium-size storage container or resealable plastic bag. Store in freezer for up to 3 months. Makes 18 mini sandwiches.