Slide a metal baking sheet into the freezer for 10 minutes, then line it with parchment. Sift the powdered sugar and chop the chocolate so both are ready to go.
In a mixing bowl, beat the butter and vanilla on medium speed until creamy and slightly whipped, about 1 minute.
Add the peanut butter and mix until fluffy and homogeneous, 1–2 minutes, scraping the bowl as needed.
On low speed, blend in half of the powdered sugar and the sea salt. Add the remaining sugar gradually until a soft dough forms that just holds together. Knead with a spatula or clean hands 10–15 seconds to smooth. If sticky, mix in 1–2 more tablespoons powdered sugar.
Cover the bowl and refrigerate 20 minutes until the mixture is firm yet pliable for rolling.
Using a 1-tablespoon scoop, portion about 30 mounds. Roll each between your palms into smooth balls and place on the chilled parchment-lined sheet, spacing slightly.
Insert a bamboo skewer or toothpick about one-third of the way into each ball. Freeze the tray for 15 minutes to set the shape well for dipping.
Melt the chocolate: Set a heatproof bowl over a small pan of hot (not boiling) water. Stir the chocolate gently until just melted and smooth, 3–5 minutes. Remove from the heat and stir in the neutral oil if using. Transfer the chocolate to a narrow cup or mug for easy dipping.
Working with 4–5 at a time, dip each chilled ball into the chocolate, leaving a neat circle of peanut butter visible on top (the classic buckeye look). Lightly scrape the bottom of the ball against the cup’s edge, then return to the sheet.
While the chocolate is still soft, twist out the skewer and gently smooth the hole with a clean fingertip or the back of a spoon warmed under hot water and dried. Refrigerate 10–15 minutes to fully set before serving.