Remove your bass pulls from the drawer using a manual or electric screwdriver. Put the screws to the side.
Put on gloves, dip a cotton ball into acetone nail polish remover, and rub it over any traces of paint or varnish on the brass pulls. You may have to repeat this process a few times if the paint it coated over the pull several times.
Run a sink of warm water and soap. Place the brass pulls in the water and use a soft soapy sponge to remove any traces of acetone and clean off any dirt. You may have to soak the brass pulls before cleaning them to remove caked-on dirt.
Remove the brass pulls from the soapy water and rinse thoroughly with warm water.
Sit the brass pulls on a towel and rub them dry. You could also use a hairdryer on low cool setting to air dry the pulls.
Open a bottle of vinegar and pour a small bit into a cup. Dip a paintbrush into the cup and paint over your brass pulls. The brass will turn immediately. If it isn’t your desired finish, paint over the brass pulls again and keep repeating until you’ve reached your desired finish.
Dry off your pulls, and dip the handles in warm water quickly to remove the smell of vinegar. Dry the brass pulls.
Pour a bit of mineral oil on a soft cloth then wipe over the brass pulls.