Melt the white chocolate chips in a medium glass heatproof bowl over a pot of simmering water on medium-low heat. Stir until melted. Remove from the heat but keep the bowl over the warm water. Set aside.
In the bowl of a stand mixer with a paddle attachment, combine the peanut butter, butter and vanilla extract. Mix together until smooth. Add about half of the powdered sugar and mix until incorporated. Add the remaining powdered sugar and mix until smooth, about 1 minute. Add the melted white chocolate and beat on medium until smooth, about a minute. Place the bowl in the freezer until the mixture is firm enough to form a ball, about 30 minutes.
Using a small scoop or spoon, roll the peanut butter mixture into about the size of a golf ball. Set on a parchment-lined baking sheet and repeat with the remaining mixture. Freeze until firm, 20 to 30 minutes. Remove from the freezer and roll the scoops into smooth balls. Plunge lollipop sticks or short, thick skewers into the centers of the balls. Freeze for another 15 to 20 minutes.
Melt the dark chocolate in a medium glass heatproof bowl set over a pot of simmering water on medium-low heat. Stir until melted. Sprinkle in the espresso powder and stir. Taste the chocolate; if you want more coffee flavor, add more espresso powder 1/2 teaspoon at a time. Keep the bowl over the pot of hot water to keep it hot while dipping.
Holding the balls by the skewers, dip the balls only three-quarters of the way into the melted dark chocolate, leaving a quarter inch of exposed peanut butter at the top (this way, it looks like a real buckeye). Let the excess chocolate drip off, then quickly sprinkle a pinch of flaky salt or pink salt right on top. Refrigerate until the chocolate is set, about 1 hour. Remove the skewers from the buckeyes. Keep in the freezer until ready to serve.