Melt butter in a small saucepan over low heat. Or, microwave in a microwave-safe bowl on 100-percent power (high) for 1 to 2 minutes.
Combine melted butter and 2 cups of the powdered sugar in a medium mixing bowl. Beat until smooth. Add peanut butter, beating until combined. Stir in milk and vanilla. Beat in enough of the remaining powdered sugar to make a firm, crumbly-looking mixture.
Roll mixture into 1-inch balls. Arrange on a tray; chill for 30 minutes.
Meanwhile, melt chocolate and shortening in a heavy saucepan over low heat. Cool slightly. Using a fork, dip three-fourths of each ball into chocolate mixture so the ball resembles a buckeye. (If the chocolate mixture hardens, remelt over low heat.)
Place balls, undipped portion up, on a tray lined with parchment or waxed paper. Chill until firm. Store in refrigerator. Makes about 72 buckeyes.