Put about 2 inches of water in a small pot and bring it to a soft boil. Add the steamer basket to the pot.
Wash the peaches, then score them with a knife (mark an “x” on the peach’s skin).
Place the peaches in the steamer basket and put a lid on the pot. Steam the peaches for 10-15 minutes, or until the peaches are soft.
Remove the peaches from the steamer basket and place them in a large bowl filled with water and ice. Let the peaches sit in the ice water for 1-2 minutes. Then, peel and cut the peaches, removing the seeds and core.
Place the peaches in a blender along with the allspice. Blend until smooth. You most likely won’t need to add any additional liquid since peaches are really juicy. If you do need more liquid to thin out your puree, add a little water, baby formula or breast milk.