Preheat your oven to 180°C (350°F) and line a muffin tin with paper liners or grease it well to prevent sticking.
In a large mixing bowl, whisk together the all-purpose flour, sugar, baking powder, and baking soda until evenly combined. The mixture should look slightly grainy but well mixed.
In a separate bowl, combine the peanut butter, milk, eggs, and melted butter. Whisk until the mixture is smooth and slightly frothy, with no streaks of peanut butter remaining.
Pour the wet mixture into the bowl with the dry ingredients. Gently fold everything together with a spatula or whisk, just until the flour is incorporated. Be careful not to overmix; the batter will be thick and slightly lumpy.
Scoop the batter into the prepared muffin tin, filling each cup about two-thirds full. You can use a spoon or an ice cream scoop for even portions.
Bake in the preheated oven for 15 to 18 minutes, or until the muffins are golden around the edges and a toothpick inserted into the center comes out clean with no wet batter.
Remove the muffins from the oven and allow them to cool in the tin for about 5 minutes. Then, transfer them to a wire rack to cool completely or enjoy warm right away.
Once cooled, the muffins will have a soft, moist crumb with a slightly sticky top and a rich peanut aroma filling the kitchen. Serve them fresh for the best flavor and texture.