How can I keep my burgers flat?

Many chefs in the USA recommend pressing a large dimple in one side of the meat patty before cooking it on the nondimpled side first, to prevent the problem you are experiencing

You shouldn't salt burgers before shaping; it tends to give them a sausage-like texture instead of a burger texture. (See, for example, this note from Cook's Illustrated). Salt the burgers, outside only, just before you put them on the grill.

I suspect that firmer texture probably makes the balling up problem worse, and that's why normal approaches like a thinner area in the middle aren't able to overcome it.

If you want the texture you get from salting them before forming, then you'll have to get a press (or re-purpose something as a press, small cast iron pan for example) or cook them with less heat (you could, for example, bake in a low oven or bag and sous vide them, then just brown over high heat).

Try a burger press, such a this one Burger and Meat Press with Wooden Handle available online at Home Depot.

To use, place on your grill to get warm, and then place on top of your patty while it cooks. They're made of cast iron, and have some weight to them, which makes keeping your patties flat pretty easy.

The chemistry of your "burger recipe" is affecting the physical 'cupping' action of the patty; as you explained here:

I'm only adding salt and pepper before i shape them

My question to add quality to my answer though, is, are you adding more salt to one side of the patty over the other? That could explain the cupping action. It is precisely like two dissimilar metals forged together and then heated again and then you notice the arching of the 'unified' piece of metal.

So, consider how you are seasoning the meat before cooking. Perhaps consider seasoning while you are cooking.

The only other option is the dead-weight/press that you see posted above; which does work well, but you are only countering the forces of the edge cupping upward (before being flipped).

I make patties every few weeks and have resorted to freezing them before frying them on my outdoor flattop. I don't find that a dimple is needed if you're making smash-style patties.

My current method:

• form 140g/5oz balls out of lean (11-17% fat) ground beef, ideally chuck, rib, etc.
• press each ball between cut squares of parchment paper using a cast iron pan to get a .75cm or ? inch thick patty (about 12-15cm / 5-6inches across)
• freeze (30 minutes - 3 weeks)

I season the patties once I flip them the first time, and I cook them at 230C/450F on a oiled flat top.

The freezing is optional, but it produces a patty that doesn't fall apart when using leaner meat. The frozen patty takes 1-2 minutes longer on a hot flattop to cook, and the texture/flavour are not significantly changed. Using "regular" ground (18-25% fat) doesn't require the freezing step.