I’ve had burgers like yours, and they are quite tasty. I don’t make them that way but my mother sometimes does and a restaurant I worked at used a similar recipe. They switched to the purist burgers and there was a revolt by the regulars who liked them that way so they offered both.
It’s a great recipe to use if you want to spread the ground beef a bit if your making the burgers for a crowd. You can make them a bit more well done to suit everyone and the burgers stay moist.
I tend to follow the “buy good meat and grill it” crowd.
But I’m wondering about the reasoning behind such comments as “using chilled hands” and “handle as little as possible.” One of my main concerns is that the patties not fall apart - which tends to happen more if I do not do at least a little smooshing while forming the patties. What harm comes from gripping your meat too forcefully? 
Also - simce no one offered it yet, I’ll mention toasting the buns lightly on the grill.
Personally, I put a squirt of BBQ sauce on mine after flipping it, but none of the rest of my family partakes.
And never underestimate the contribution that can be made by some decent cheese, instead of those squares of processed stuff. If the cheese is in square slices, fold the corners up to keep more of it on the burger instead of just dripping onto the flames. The round slices are great in this respect. I prefer colby-jack.
I think it changes the texture of the meat. I’ve seen people roll the meat into little balls and sort of squish it through their fingers then flatten it. I don’t think it affects the taste but it makes the hamburger almost look like processed beef patties. The cold hands probably so the burgers don’t fall apart.
Once in high school (about 16 years ago) I was cooking dinner for my siblings and I, and I think I made burgers similar to the recipe you described. Whatever I did, they were the best burgers I have ever had before or since (when your younger siblings compliment you, you know they’re good), and I’ve despaired of ever recreating the recipe. Thank you. I’ll have to try this recipe and see if I can recreate the taste.
Oddly enough the best advertisement for simple burgers that I have seen was on English cook Delia Smith’s show. She stated that she thought it was easier to cook great burgers than great steak even with the same meat. Here are her half pounders - once you get the coarseness of the mince right (quite a bit coarser than regular mince) they are infallible.
A lot of folks seem to think you’re suppose to make a hamburger by grabbing a hunk of ground meat, kneading it into uniformity, forming a sphere, then flattening the sphere.
I contend that this makes the meat too dense. It ruins the taxture, and doesn’t allow you to grill the burger properly. . .slight crusty on the outide with good, moist meat on the inside. To cook the middle of a dense burger, you need to overcook the outside.
When I say “handle the meat as little as possible”, I mean. . .as little as possible so that it’s not falling apart. Not some minimal amount so that you have hunks of loose meat falling through the grate.
This is food here, though, not the science of rockets or the surgery of brains. Try both methods next time you make burgers, and see which you prefer.
Also, I should mention that some people make the mistake of forming a burger that is roughly the dimensions of what a burger should look like on the bun. When you’re done grilling this, what you’re left with is a hamburger that is too spherical, and puffed up.
To counteract the puffing phenomenom, one should make the raw patty flatter and thinner than what the want the cooked burger to be.
If you dish it out in the middle a bit with your thumbs, when you cook it it comes out flat.
I am with you.
Our recipe has onions, oatmeal, egg, and spices in it. The meat is a medium for taste. Top it with sauteed mushrooms in a ring of grilled red pepper, covered in cheese, add the usual condiments, fresh tomatoes, lettuce and viola! tastiness ensues.