Baking – Is it possible to cream clarified butter with sugar? Will it have the same benefits as shortening and oil

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.

Your recipe is suspect. Melted butter is the same in chemical composition as softened butter. The two react a bit differently in recipes due to the way that they interact with the other ingredients to impart textures: in short, the creamed butter will hold microscopic bubbles that the fully melted butter will not. Adding egg yolks will help the melted butter incorporate, and probably lead to more cakey cookies (compensating for the flatness you get from melted butter), but the effect is hard to isolate.

As for brown butter, what happens is that as moisture evaporates from the butter, the boiling point increases (similar to what happens when making caramel or candy). As the boiling point of the butterfat increases, the temperature of the butter solids (which consist of lactose and milk proteins) begin to caramelize (the sugars) and undergo a maillard reaction (the protein). Both of these reactions will impart unique flavors to the butter, yielding the distinctive brown butter taste.

As the butter heats, the integrity of the fat is damaged. This occurs to all fats, which is why you can only use a batch of fat for deep frying a few times before it needs to be discarded.