That is the only way to do this as you said, getting a piece of laminate cover it, or go custom to make it a a one piece.

Another way to save some money is to put the wood and paint it trying to match the counter-top, push the counter forward and call it a day. Or put a shelf along the back wall so you don't see much of that wood and that pretty much it.

Good luck

Unless it really bugs you, I would leave it. A lot of folks have the W/D stick out beyond the depth of the counter and I think it looks fine. But if you're looking for a more built-in look, I'm afraid that will be a custom job.

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You clearly need a counter stretcher.

Failing that, keep in mind that it's a laundry room, not the Taj Mahal.

So, if there's no sink in the counter, you could fill-in with wood and matching laminate and live with a seam that is never completely solid. Or fill in the area behind with 1x6 Azek or a similar PVC wood substitute (no need for laminate if they are both white).

But if there's a sink, you'll need to come up with a water-tight solution, so custom build.

Or DIY laminate. It's not difficult to apply laminate; it's tricky and a bit messy, but not rocket science.

Does the counter have the integrated backsplash? If it does, then pull the counter top forward and install a raised shelf the the front edge of the shelf supported by the top edge of the backsplash. Support the back edge of the shelf with a ledger board so it is easy to remove for access to the water valves, cleaning, repairs...

Also from Ikea - tabletop Linnmon 59" x 29 1/2"

I got this advice on Houzz from Susan St. Pierre in 2014