The finish is Watco Danish oil wet sanded at 600 grit, wiped off, re-applied very heavily, and let stand until tacky (a couple of hours to overnight). Buff with a soft cotton cloth, let dry overnight, and repeat until it simply won't absorb any more...typically 2 or 3 cycles. A rub with x-fine steel wool soaked in the oil works well in place of the wet sanding...personal preference.
It sometimes bleeds a bit a couple of days later, but another soft cloth buffing shines it right up, so I have to be careful to let it cure for a week+ before delivering.
Mesquite has a fair bit of variation in coloration depending on where it grows.