What are the breaks like? If they’re jaggy and diagonal kinda think then decent wood glue and plenty of tightly wrapped tape to clamp it should be enough. If they’re more like clean square ended breaks where it was originally joined you have more issues. Could try and worktop joining bolt on the underside, plus glue. Any white / PVA will be fine.
I wouldn’t bother with dowels then, if they’re jagged splits there should be plenty of surface area. Could screw through for belt and braces. See technical illustration:
What are the breaks like? If they’re jaggy and diagonal kinda think then decent wood glue and plenty of tightly wrapped tape to clamp it should be enough. If they’re more like clean square ended breaks where it was originally joined you have more issues. Could try and worktop joining bolt on the underside, plus glue. Any white / PVA will be fine.