Stir together the powdered sugar, peanut butter, and vanilla in a mixing bowl until a cohesive dough forms. Place bowl in fridge to chill while you melt the white chocolate.
Add the white chocolate and oil to a microwave-safe bowl. Microwave for 45 seconds, stir, then continue heating in 15 second intervals until melted and smooth. Spoon 1 TB of melted white chocolate into the bottom of each muffin liner. Chill in freezer while you work on the peanut butter filling again.
Take peanut butter mixture out of the fridge and portion into 10 even balls. Press to flatten the peanut butter balls into pucks. Place one peanut butter disc on top of the white chocolate layer in each muffin cup.
Remove muffin pan from fridge and pour remaining white chocolate on top of each peanut butter cup, until all peanut butter is covered. Chill until set before removing from the pan.