Best way to mount a wooden tabletop to a flat surface
A relatively unattractive method would be to use small right-angle brackets. You could also attach a cleat to the sides of the drawer assembly, driving screws into the drawer assembly horizontally and into the desktop vertically. Less unattractive that way. The more expensive and more sophisticated method would be to use a pocket hole drill jig:
Lowes Pocket Hole Drill Jig
which would require sufficient thickness of wood in the drawer assembly sides.


There are ramifications to each of these methods depending on your restrictions regarding visible screws. Even a simpler method of drilling into the desktop, fastening vertically, then installing a plug and refinishing the surface will mean screws that are not seen, but may not meet your requirements overall.