Why does sugar turn brown and buttery-tasting with no protein at all?

Because caramelization doesn't need protein at all. It is the browning of sugar used in cooking for its butter-like flavor and brown color, and it is pyrolytic: heat itself breaks the sugar down, and the pieces react with one another, instead of reacting with amino acids. The browning on a seared steak or a loaf of bread is a different process, the Maillard reaction between amino acids and reducing sugars, which the French chemist Louis Camille Maillard first described in 1912 while trying to reproduce protein synthesis. Both are non-enzymatic browning, but only one needs protein.

To caramelize, sucrose has to be heated above 140°C, often helped along by an acid like citric acid. The heat splits sucrose into its two simpler sugars, fructose and glucose, and sets off a complex, still poorly understood cascade that produces hundreds of compounds. Three families of brown polymers, called caramelans, caramelens and caramelins, give the color, while volatile chemicals such as diacetyl, known for its intense butter-like taste, give caramel its flavor.

Conditions in the pan change everything. The reactions are temperature-dependent, impurities such as the molasses left in brown sugar greatly speed them up, and they run slowest near neutral pH and faster in acidic or basic conditions. With too little water, though, the dehydrated sugar simply turns into carbon. Cooks see the slow side of caramelization with caramelized onions, the base of French onion soup, which need 30 to 45 minutes of cooking.