Four 4-ounce ice-pop molds or six 3-ounce molds, 4 or 6 ice-pop sticks
Prepare a grill or large grill pan for high heat. Bring the ginger, sugar and 1/4 cup water to a simmer in a small saucepan. Cook on medium-low for 10 minutes. Let cool completely at room temperature, at least 30 minutes.
Meanwhile, brush the peach halves all over with the butter. Place them cut-side down on the grill, and grill until very charred, about 5 minutes. Flip the peaches, and grill until the rounded side is charred in spots and the peaches are tender but not falling apart, about 5 minutes. Transfer to a plate to cool completely, about 20 minutes.
Put the cooled peaches, preserves, 1/2 cup of the almond milk, lemon juice and a small pinch of salt in a blender. Strain the cooled ginger syrup into the blender, pressing the ginger pieces in the strainer with the back of a spoon to extract as much flavor as possible; discard the ginger. Puree the peach mixture until completely smooth, scraping down the sides of the blender partway through if needed. Transfer the mixture to a large liquid measuring cup with a pouring spout.
Pour the mixture into the ice-pop molds, leaving 1/4 inch of space at the top (the mixture will expand). Insert the sticks. Freeze until solid, 5 hours to overnight.
When ready to serve, put the remaining 1/2 cup almond milk in one drinking glass and the almonds in another. Unmold the ice pops, and dip the top of each into the almond milk, then into the almonds. Serve immediately.
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