I sanded it flat/smooth with 80 grit on a jitterbug sander, followed by one good coat of Valspar white primer.
I used Olympic premium interior latex, matched to the original colored melamine, from inside the cabinet. Sprayed out of an HVLP gun. The mix was about 85% paint, 5% Floetrol (flowing agent), and 10% water.
It looked rougher in the first couple of coats, and I ended up sprayed a total of 5 thin coats. After leveling out, the finish is VERY smooth.