Preheat oven to 350 degrees. Line a muffin tin with liners or spray with non-stick cooking spray.
In a stand mixer or large bowl, beat the butter and sugar until light and fluffy, about 2 minutes. Beat in the eggs, one at a time, until just mixed in. Add the vanilla.
In a medium bowl, combine the flour, baking powder, salt, and pumpkin pie spice. Stir until well combined.
Mix a quarter of the dry ingredients into the butter and sugar mixture, followed by a third of the milk. Continue mixing in the remaining dry ingredients and milk alternately, ending with the dry. Mix until well combined and smooth, but don't over-mix. The batter will be very thick.
Scoop enough batter into each muffin tin so that the top of the batter is even with the rim of the cup. (I like to use a large cookie scoop for this.)
Bake the muffins until firm to the touch, about 25 minutes.