I am using kitchen cabinets to create a home office. I want to run the baseboard around the walls and continue onto the cabinets, thus hiding the toekick and making the cabinets look more like furniture.

My cabinet doors and drawers do not allow any clearance below them, so I am at a loss as to how to attach the baseboard.

I've tried to find information about how to span the toekick with baseboard. Any ideas? Photo attached shows how I'd like it to look.