Remove the old countertop to measure the existing base cabinet as well as the space for the new countertop. After closing and detaching the water valves below, use a utility knife to cut the caulk strip around the sinks. Lift out and remove the old sinks.
Carefully cut the caulk seams between the countertops and bathroom walls and then unscrew and remove the countertop from the underlying cabinet base.
With the old counter removed, create a template that represents the top of the cabinet base and its relationship to the bathroom walls. Place strips of wood veneer along the edge of the cabinet and against the walls. Fasten the wood strips together with a hot-glue gun. Write on the template to indicate the orientation of the template and also include a reminder to later include a 1" overhang on the front side of the new countertop.
Prepare to pour the concrete by constructing a laminated plywood box form. From the template, trace the dimensions, adding the 1" overhang onto a board of laminated plywood called melamine. Although this serves as the base of the form, it actually represents the top of the new countertop, which will be poured upside-down.
The template indicates that the bathroom walls are not perfectly square, so trim the end of the board at a slight angle using a circular saw.
Cut the melamine to form 3" wide sidewalls on a chop saw. Form the box, minus a top, by screwing the sidewalls to the base.
Address the pre-cast sinks by caulking down custom sink molds onto the base. Also caulk a small plastic cylinder onto these molds that later creates a drain tube.
Because the soupy concrete would simply run down the sides of the sink molds without them, add a second tier to the form by building a pair of melamine containment boxes around the sink molds. Attach these to the base form with wood braces and screws.
To give the concrete added structural integrity, cut and place segments of rebar lengthwise within the form.
With the form ready, prepare two batches of concrete. First, portion out Portland cement, sand, silica powder and coarse aggregate into several plastic buckets.
Pour the ingredients into a portable mixer. Add a special agent to keep the mix from clumping. With the ingredients churning in the mixer, add water until achieving the consistency of cake batter and dump the wet concrete into a wheelbarrow.
Agitate the wet concrete with a shovel and use a metal scoop to pour it into the form. Evenly distribute the aggregate with your hands and pull up on the rebar so it suspends in the middle of the liquid concrete. Then, use a float to smooth the concrete flat.
With the bottom tier full of concrete, screw three melamine cap-boards onto the openings away from the sinks. These caps prevent the concrete from overflowing when adding to the second tier around the sinks.
After mixing a second batch of concrete, fill in the rest of the form, covering the sink molds. Again, distribute the aggregate and smooth the surface with the float. The concrete is allowed to set for a minimum of two days.
After the concrete has cured, unscrew and remove the cap-boards. Then, flip the heavy slab over onto a wheeled cart and proceed to remove the sink molds.
To polish the concrete countertop to a smooth finish, use an abrasive pad and a water-feed to smooth the sides and concave sinks. For the large, flat surfaces, use a disc sander fitted with diamond discs of varying grit. Throughout the polishing, the running water feed helps prevent material from clogging the sanding surfaces.