I made a pass with the engraver then changed the laser focal point to the deepest engraving mark. I repeated this process 3 times to ensure my channels were deep enough to fill with epoxy.  Depending on the wood you may need more or less power/passes.  
I cleaned the board up with some brushes and towels to remove some of the carbon.  

Inject colored Epoxy into the engraving marks with your preferred colors.  I used a table top epoxy which takes an extended period to cure and I used mica powder to color the epoxy.  Quick cure epoxy would be suitable for this project.  Dye or mica will work well to color the epoxy.  
If you are not comfortable using epoxy you can use UV resin.  Note that the UV resin may not be as hard so you may need to apply a protective coating to your finished project.  

As with any project you need to add those finishing touches.  Sand the wood with several increasing grits of sand paper.  I used 80, 120, 150, 220 grit.  Then I oiled the board.  Use your favorite cutting board oil.  Alternatively, you could also apply a top coat/sealer like urethane.