I'd go to Formica's web site and get their 1-800 phone number for their head office. Phone them up and ask to speak to someone in their technical support group if they have one. They would know what solvents, if any, would dissolve plastic laminate.
I googled Formica to see what it was made of:
and found this:
"It is composed of many layers of resin-impregnated kraft paper
and topped with a decorative layer protected by melamine, then compressed and cured with heat to make a hard, durable surface."
Which tells us that the protective surface of the stuff is melamine plastic.
Googling "dissolves melamine" came up empty, but Googling "reacts with melamine" produced a bunch of hits, including:
"Formaldehyde reacts with melamine
to produce resin."
"In our process, the sulfuric acid reacts with melamine
to precipitate (C 3 H 6 N 6 ) 2 H 2 SO 4 2H 2 O."
"Polyvinyl butyral has the ability to thermoset into a hard durable film and also reacts with melamine
"HMF reacts with melamine
to form a partially. polymerized resin of low viscosity."
"As a consequence, it may be assumed that the unsaturated polyenes formed when PCA dehydrochlorinates reacts with melamine
and/or with its condensed forms..."
Me thinks that the most likely candidate is sulfuric acid. Maybe formaldehyde.
Perhaps someone put a leaking car battery on your counter top. The acid in lead-acid car batteries is sulfuric acid.
Maybe liberate some of those small laminate sample chips from any hardware store and apply battery acid to it with a Q-tip to see if you can reproduce the results. Any auto electric shop will have battery acid.
I don't know where you can get formaldehyde, but Googling formaledhyde says that formaldehyde-based fluids are used for embalming human corpses, and formaldehyde is used in aquariums to kill certain fish parasites. Try your local pharmacy, too, as the pharmacist would likely know where to get it.