In a large bowl, stir together the butter and peanut butter until there are no lumps of butter.
Add the powdered sugar, vanilla, and salt. Mix with a spoon or your hands until thoroughly combined.
Wrap the peanut butter filling in plastic wrap and chill for 30 minutes, or until firm enough to roll into balls. (You can chill it for 2-3 days.)
Scoop and roll the peanut butter mixture into small balls. I used a 1/2 ounce cookie scoop.
Chill the peanut butter balls for about 15 minutes.
Melt the chocolate at half power in the microwave, stirring every 30 seconds.
Use a baby spoon, plastic fork, or dipping tool to submerge each ball in the melted chocolate. Tap the spoon against the side of the bowl and let excess chocolate drip back into the bowl.
Use a toothpick to push the bottom of the chocolate ball off the spoon onto a silicone mat or parchment paper.
Quickly top the dipped balls with sprinkles before the chocolate sets. I find that I can usually do 3-4 at a time.
Since the peanut butter filling is cold, the chocolate should set quickly.