Seperating your cutting board strips into two groups, no wider than the max capacity of your planer, glue the strips together using Elmer's® Carpenter's® Wood Glue MAX. I like using the Elmer's® Carpenter's® Wood Glue MAX version because it's waterproof, which is very important since these cutting boards will definitely be coming into contact with water when they got washed after use.
Lay a thin bead of glue down on each of the strips and use a chip brush to spread the glue evenly along the strip. Clamp the strips together and use some hearty pieces of wood as cauls to keep everything in line. Let the strips sit overnight and repeat this process for the second batch of strips.