Pre-cut handle halves. All dowel holes are 5mm and use 5mm bamboo rods as dowels (marshmallow roasting sticks). Pretty strong stuff and cheap (e.g. Amazon).
Drill dowel holes first and screw down a few holes to hold the cut-out handle parts (also the "island" in the middle). Zero reference from top surface to assure pocket depth. Handle material must be planed or milled first to exactly 18mm (0.709") thickness.
Glue and dowel both halves together with middle layer, clamp. Then sand all the steps and machining ridges away (random orbital sander and Dremel with small flap wheel) and finish. Danish or Tung Oil recommended, not laquer.
Practical and decorative mallet for chiseling and mortising, about 1.2 pounds (depending on wood species)
Drill 6-10 dowel holes into spoilboard (using vectors from "middle layer" file) and press the two mallet pre-cut halves onto temporary dowels. If friction is not sufficient to hold them down, use a few drops of CA glue.
Then carve the outer shape with a 1/4" ballnose bit
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Optional: cut a middle layer (~1/4" thick) from contrasting hardwood
Cut head halves from 31.75mm (1.25") stock (slightly thicker is O.K.). Zero reference from top surface. Then glue handle halves into head halves and clamp. Result should already be almost flush.
Material must be crack free, if necessary fill cracks and crevices with medium CA glue or epoxy. Sample here is Mulberry but Oak, Beech, Hickory or Maple are good choices. If using oily exotics make sure the glue joints will hold.