In a large mixing bowl, combine 3 1/2 cups powdered sugar, entire 15-ounce jar of creamy peanut butter, and 1/4 cup very soft unsalted butter. Add 1 teaspoon vanilla extract and 3 tablespoons milk. Beat with electric mixer on medium speed until smooth, thick, and well combined.
Gently fold in 1/3 cup of the mini Reese’s Pieces into the peanut butter mixture for crunchy bursts throughout the center.
Cover the bowl with plastic wrap and refrigerate for about 30 minutes to firm up the mixture. Scoop tablespoon-sized portions and roll into smooth balls. Place on parchment-lined baking sheet.
Melt 3 cups bittersweet chocolate chips with 1 tablespoon canola oil in a double boiler or microwave-safe bowl. If microwaving, heat in 30-second intervals, stirring until smooth.
Using a fork or dipping tool, dip each peanut butter ball into melted chocolate, covering fully. Let excess chocolate drip off and place back on parchment paper.
Before chocolate hardens, sprinkle remaining 3 tablespoons of mini Reese’s Pieces on each truffle. Let set at room temperature or refrigerate to firm.