Cookies – this dipped powder cookie called

This looks to me like the symptoms of too much flour - probably way too much.

Measuring baking ingredients by volume instead of weight is always a crapshoot, although it shouldn't be that far off - my guess is that either the flour was heavily compacted, or perhaps the baker's mind wandered off and she accidentally added an extra cup.

Overmixing (i.e. by using an electric mixer) is a common problem with cookies but the symptom of that is a hard and gritty cookie that doesn't rise - not one that rises too much and has unbaked flour in the center. As far as I know, that can only happen with a huge amount of flour. Obviously, too much flour would also result in a much denser dough.

What you ended up with seems to be more like a quickbread - almost a scone - and there is indeed not an awful lot of difference between the two aside from the ratios and the creaming of butter.

Excess flour probably wouldn't result in a stickier dough, but stickiness is more due to temperature than anything else. If you're finding the dough too sticky to mold then make sure it's thoroughly chilled - that will make it easier to work with.

Sounds an like you may just need more flour. That recipe has more fat per flour than common cookie recipes - for example, the canonical chocolate chip cookie recipe has 10 oz of flour for 1 cup of fat, while yours is only about 8 oz flour per cup of fat. So I'd definitely expect the dough to be on the soft side to begin with, and since the fat softens at it warms up, as you've seen, it just gets worse.

If your kitchen is on the warm side, it's possible that you'll also need to chill in the freezer instead of the fridge, but I'd certainly start with more flour (or less fat).