Transfer ice cream and parchment lining from larger pan to a flat surface. Cut ice cream into 12 squares, 2 1/2 inches each. Transfer to a parchment-lined baking sheet; freeze at least 3 hours. Repeat with smaller pan, making 9 squares.
Break graham crackers in half to make 2 1/2-inch squares. Spread one side of each with about 1 1/2 teaspoons jam; freeze until firm, about 45 minutes (this keeps finished pops neat). Sandwich ice-cream squares between graham crackers, jam facing ice cream. Insert a wooden pop stick into each.
Place peanuts in a bowl (if using); dip each side of the pop in the nuts. Pat gently with your hand to adhere. Pops can be frozen at this point, wrapped in plastic wrap or layered between waxed paper in an airtight container, for up to 2 weeks.