What is the best way to remove layers of paint from a dresser?

Use Citristrip which is a safe non-toxic paint striper.

Apply stripper then apply a layer of waxed paper over the stripper. After you let it set awhile pull it off. The paint should stick to the waxed paper.

Enamel paint has varnish added to it. Pain in the b*tt to remove. You will need a strong paint stripper. Lots of VOC and flammable. Use it outside, rubber gloves, eye protection, face mask. Safe strippers will not work on enamel paint!

Strypeeze Paint & Varnish Remover or Zip-Strip 32oz Premium Paint, Varnish And Stain Remover or a heat gun.

Try with an electric thermic paint remover before any chimical product. It may crack and go...