Remove any fixtures in the existing counter. This includes sinks and installed small appliances such as hot water taps.
Clean the existing surface with a degreaser and sand to scuff the finish. Wipe with a damp rag and allow to dry.
Plan your wood cuts. Lay out the wood so the seam falls somewhere inconspicuous -- corners are good, or the front and back of the sink works as well. Measure the area to be covered, including a front overhang of 1/2-to-1 inch. Mark off the necessary holes for the sink, faucet or other appliances and make your cuts. Cut from the underside of the wood to avoid chipping the surface.
Spread paneling glue across the existing subsurface with a foam roller. Apply an even coat. Place the first piece of wood, sliding it into place.
Apply two-part epoxy to the seam edge of both pieces of wood and slide the second piece into place. Butt it up very snugly against the first piece until epoxy bubbles up from between them.
Press the wood firmly into place. Use a rolling pin or a linoleum roller to ensure an even bond. Use a carpenter's level to make sure the wood is seated evenly on the subsurface, rolling any raised areas flat. Allow to dry.
Sand the entire countertop but pay special attention to the seam. Sand off the excess epoxy and sand both pieces of wood until both sides of the seam are level. Install hardwood trim around the edges to hide the plywood layers.
Dust the counter and wipe with a tack cloth. Apply your finish of choice. Tung oil provides moisture protection but it must be followed with repeated mineral oil treatments to be food safe.