Line a 12-cup muffin tin with paper or silicone liners.
In a medium bowl, combine peanut butter, sifted powdered sugar, softened butter, and vanilla extract. Mix until smooth and well combined.
Press about 1 tablespoon of the peanut butter mixture into the bottom of each muffin liner, creating an even layer.
Place the muffin tin in the freezer for about 10-15 minutes to firm up the peanut butter layer.
While the peanut butter is chilling, melt the semi-sweet chocolate chips and coconut oil (or vegetable oil) together. This can be done in a microwave-safe bowl in 30-second intervals, stirring between each, or in a double boiler over simmering water until smooth.
Once the peanut butter layer is firm, spoon about 1-2 tablespoons of the melted chocolate mixture over each peanut butter layer, ensuring it covers completely.
Return the muffin tin to the refrigerator for at least 30 minutes, or until the chocolate is completely set.
Once set, remove the cups from the muffin tin. Serve chilled.