Speaking "vaingloriously" means to speak:

When someone speaks "vaingloriously," they are doing so in a boastful manner, often characterized by excessive pride and self-promotion. This term derives from "vainglory," which refers to an inflated sense of self-importance and a desire to gain recognition or admiration from others. In contexts where this word is used, it typically suggests that the speaker is overemphasizing their achievements or qualities, leading to a tendency to talk about themselves in a way that seeks validation and shows off their accomplishments or status. Hence, the meaning aligns perfectly with the choice that describes speaking boastfully.