As I was to read it. Until I scrolled down I thought you made the dog on the Glowforge! Great job. Getting good engraving from photos is an art unto itself.
Noooo! If you plan to use it as a cutting board, just use the board oil. Food-safe finishes are a whole topic of study but cutting board dressings like oil and wax are made-for-purpose to be food safe and, as a rule, stain is not. And while there may be some food-safe stains out there, once the board gets some cuts in it, the real color will show through, making the knife marks stand out.
Which is why you don’t want a film-forming finish either. Most of those are food safe when cured but that applies to incidental contact. Apply a knife edge to some of those and you end up eating flakes of the finish.
Keep the natural color and stick to food-safe dressings (not finishes) is best for cutting boards.