Preheat your oven to 180°C (350°F) and line your muffin tin with paper liners or grease it well.
In a large bowl, combine the creamy peanut butter and sugar, then whisk or stir until the mixture is smooth and slightly fluffy, and you can smell the toasty aroma of peanut butter.
Add the eggs one at a time, whisking well after each addition to create a glossy, cohesive batter.
Stir in the vanilla extract until fully incorporated, filling the kitchen with a warm, sweet smell.
In a separate bowl, sift together the flour, baking powder, and salt to ensure even distribution and prevent clumps.
Gradually fold the dry ingredients into the wet mixture using a spatula or spoon, mixing just until no streaks of flour remain. The batter should be thick but moist.
Scoop the batter into the prepared muffin tin, filling each cup about three-quarters full, and listen for the satisfying plop of batter dropping in.
Bake in the preheated oven for 15-20 minutes, or until the tops are golden and a toothpick inserted into the center comes out clean with a few moist crumbs.
Remove the muffins from the oven and let them rest in the tin for 5 minutes, allowing the steam to settle and the crumb to set.
Transfer the muffins to a wire rack to cool slightly, revealing a tender, slightly crackly top and a moist interior.
Serve the muffins warm or at room temperature, perhaps with an extra dollop of peanut butter or a drizzle of honey for added indulgence.