This probably old hat for most but just in case this is how I make buttons to attach table tops. I like to use Oak because it splits easily. Most of the time the I will chop the mortise with a 3/8" pig sticker. For that size mortise a 9mm tenon works so a 19mm thick hunk of Oak is a good starting place. I will usually cut the stock into 30mm wide 70mm long pieces. Mark two lines near the center of the stock the length of the desired tenon:
Transfer one line to the top and the other to the bottom and mark the center line on both sides:
Saw to the Center line from the top and the bottom using the offset lines as reference and then split the button by propping one end on something and giving it a good whack:
The split button, just needs a pilot hole drilled and I will usually counter sink the pilot hole:
This is the fastest way I've found to make a number of buttons. I figure I need at least ten maybe fourteen buttons for the bath vanity.