In a large mixing bowl, combine the softened butter and peanut butter. Beat with a hand mixer or stir firmly with a wooden spoon until smooth and well blended.
Add the powdered sugar about 1 cup at a time, along with the vanilla and salt if using. Stir after each addition until the mixture starts to come together into a thick, soft dough. It should feel like play dough—firm enough to hold a shape but still easy to pinch. If it’s too sticky, add a couple more tablespoons of powdered sugar.
Scoop out tablespoon-sized portions of the peanut butter mixture and roll them between your hands into smooth logs, then gently pinch and round the ends to form an egg shape. Place each egg on the parchment-lined baking sheet, leaving a little space between them.
When all the eggs are shaped, slide the baking sheet into the refrigerator and chill for at least 45 minutes, or until the eggs are firm enough to pick up without bending. For easier dipping, you can chill them 1–2 hours.
Near the end of the chilling time, place the chocolate chips and vegetable oil or shortening in a microwave-safe bowl. Microwave in 20–30 second bursts, stirring after each, until the chocolate is fully melted and smooth. (You can also melt the chocolate in a heatproof bowl set over a pan of barely simmering water, stirring until glossy.)
Take about half of the chilled peanut butter eggs out of the fridge, keeping the rest cold so they stay firm. Using a fork or dipping tool, lower one egg at a time into the melted chocolate, turning to coat completely. Lift it out, tap the fork gently on the edge of the bowl to let the extra chocolate drip off, then slide the coated egg back onto the parchment-lined baking sheet. Repeat with the remaining eggs, working in batches so the centers stay cold.
Once all the eggs are coated, return the baking sheet to the refrigerator and chill until the chocolate is fully set and glossy, about 30–45 minutes. If you like the look from Grandpa’s kitchen, you can cut a few eggs in half once they’re set and arrange them back on the parchment so everyone can see the peanut butter filling.
Keep the finished peanut butter eggs stored in a single layer on the parchment-lined baking sheet or in a covered container in the refrigerator. Let Grandpa—or whoever is on fridge duty—guard them until dessert time so they stay cold and special. They’ll keep well for about a week, though they rarely last that long.