Cookies – mixed egg and bicarbonate of soda

If they're tangier than you'd like that would be due to the acidity of the cream of tartar. While most recipes for Snickerdoodles do in fact us cream of tartar and baking soda for a homemade form of baking powder (most likely due to the fact that snickerdoodles are fairly "old"-style cookie), a few I looked at are using baking powder and no cream of tartar.

Here are a few things to know and a suggestion:

Acidic doughs do not spread easily and do not brown easily. Using the combination of cream of tartar in the 2:1 ratio w/ baking soda for leavening not only causes them to puff but with the higher acidic ratio it is also likely to help in keeping them more "cakey" and prevent them from browning as much.

You could try cutting back the cream of tartar slightly and seeing if that helps (possible drawback could be the soda making a more pronounced bitter soapy taste if there isn't enough acidity).

Or

Replace the cream of tartar and baking soda with baking powder. Baking powder by volume isn't as powerful as baking soda because of the fact it contains soda, two dry acids, and cornstarch. 1 teaspoon of baking powder will leaven 1 cup of flour (vs. 1/4 teaspoon of baking soda to leaven a cup of flour). If your recipe calls for 2 cups of flour then use 2 teaspoons of baking powder and cut out the cream of tartar and baking soda.

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.