Self-indulgently tells you how someone does a thing: they do it in a way that lets themselves enjoy a pleasure they do not need, often a little too much. They may stretch in the sun self-indulgently, eat self-indulgently, or linger self-indulgently over a song they love. The word carries the same mild-to-strong disapproval as self-indulgent, though people also use it lightly about themselves. Put it with a verb. It is fairly formal; in easy speech you might just say she was spoiling herself. It does not mean they acted as if they were important — that is self-importantly, a different fault.