Place the drained nuts, dates, and 2 cups filtered water in a high speed blender. Pour blended liquid into a nut bag or cheesecloth over a bowl and squeeze out milk.
Measure 1 3/4 cups of nut milk into a bowl, reserving extra for another use. Stir in melted coconut oil, ginger, cinnamon, vanilla, and salt.
Drop chopped peaches into the empty popsicle molds. Pour nut milk mixture up to fill line. Insert sticks and freeze overnight.