In a saucepan, combine the water, honey, and rum. Bring to a boil. Set aside at 3°C/40°F [in the refrigerator].
Cream the softened butter with the sugar. Gradually add the eggs. Fold in the ground pistachios and pistachio paste. Mix until a smooth, homogeneous cream is obtained.
Slice the croissants horizontally at the base. Generously brush both cut sides with the honey syrup. Using a piping bag fitted with a flat (ribbon or train track) tip, pipe 40 grams of pistachio cream onto the bottom half of the croissants, then place the top half back on. Spread 30 grams of pistachio cream over the top of the croissants. Cover the surface of the croissants with whole pistachios. Place on baking sheets lined with parchment paper.
Bake about 20 minutes at 160°C/320°F in a convection oven, or 190°C/375°F in a standard oven.
Cool on a wire rack.
Dust the croissants with powdered sugar.