Miele makes a very thin induction cook top

Here is an inexpensive option. I believe this is a Korean product with a good track record. Two zones, 1800 watts and $229. Cooktops are slim, generally only 20-1/2 inches deep. Ikea has one 30"x20" for 995. The UK sight has a zoneless last gen AEG 28x20 for about 600 if you know someone coming back from a trip over. FRAMTID HINF4T

Here is a link that might be useful: Inexpensive induction

Do you mean slim front to back or slim top to bottom?

AEG also makes a longer single element deep unit than the one Dan mentioned, and I've seen ones with traditional elements as well. I think some that are sold in North America.

If you were talking about top to bottom, there's also ventilation space to consider. Some of the American brands are meant to be put over standard cupboards where you're supposed to leave the top of the cupboard empty. If you're installing over drawers, there are a lot of units that you can put in with minimal space underneath and a plywood "heat shield" to separate it from the drawer. For this, you need a channel behind the drawers for the air volume, which also gives you room for the cord.

I second the comment by billp1 - Miele makes one of the thinnest out there right now.

Anthony
Appliance Buyer's Guide

Euroline in Canada offers the 36x16" 3 area AEG 98001-K, a zoneless unit. A bit larger than the unit in the video.

If by "slim" you refer to depth below the countertop, the LG model LCE30845 is less than 2-1/4" deep. In addition, because the cooling fan does not exhaust to the undercounter area but rather through a slim slot above the counter, very little clearance is required below the unit.

Yes, I mean thin as shown in the video where it looks almost as thin as laying a cookie sheet flat on the counter. The video implied you can just set it on a counter, plug it in and immediately start using it like a very flat two burner hot plate.

In the United States, an appliance that plugs into a standard wall socket would be limited to about 1500 watts; you would need a 220-240V, 30-40 amp, wall socket for much more power than that.

Too bad about American home power. In other countries you don't need different plugs. You can plug a 2 watt night light into a 240v plug.

Hm... I interpreted it differently. I thought that unit that looks like a cookie sheet was actually installed into the counter. Do you understand Korean? Did they say it was the whole unit on top of the counter? Without any fan? That would be interesting.

I watched it again and it does go into the counter. At first, I though they were showing two different models.
It went by fast and all they show is it sitting on the counter and then the woman plugging in an outlet and cooking right away. They skipped the part where a construction crew cuts holes in the counter.
It would be nice if it was that thin that it looked built in without and installation.