Preheat the oven to 350º F(180°C). Spray donut pan with non-stick spray. Set aside.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and allspice. Set aside.
In a separate medium bowl, whisk together milk and vinegar. Let the mixture stand at room temperature for 5 to 8 minutes. When it is ready, the milk will be slightly thickened, and you will see small curdled bits. Set aside.
Beat with an electric mixer the butter and brown sugar on medium speed until creamy.
Add molasses and vanilla, scraping down the bowl's sides and bottom as needed; mix to incorporate. The mixture could be piecey and not fully combined. That’s ok.
Reduce mixer’s speed to low. Add half of the flour mixture; mix to incorporate. With the mixer running slowly, pour the milk mixture, then add the remaining flour mixture. Mix until just combined. Scrape down the sides and bottom of the bowl as needed.
Spoon the batter into donut cavities, filling half of the way full. Note: For ease, I highly recommend using a large zipped-top bag. Cut a corner off the bottom of the bag and pipe the batter into each donut cup.
Bake for about 10 - 11 minutes, or until a toothpick inserted in the center comes out clean. Cool donuts for 2 - 3 minutes, then transfer to a wire rack. Re-grease the pan and bake the remaining donut batter.