You are asking for a verb to concisely relate a complex set of facial/eye/brow expressions. I don't think there is one. In fact, I submit, if you asked someone to draw a "scowl", you would get a whole array of pictures (eyes, brows, mouths, and teeth etc.) - all different. However, there are verbs that vividly imply the "look" on ones face - at least to those with active visual imaginations.
The "facial" expressions used by Puss in the Disney Shrek film are expressions of solicitation. The brow's upward inflection is suggestive of having a "begging" posture (being of lowly/poor estate) or of "humbly asking" (request from a lower rank). The facial expression also conveys sincere need (it's all in the eyes) in an attempt to "solicit" pity or a merciful response.
Several descriptive verbs that suggest similar composites of facial features are:
to beg, or to beseech, to supplicate, or to plead, to entreat, or to implore.
One example: The entire look on her face implored him to give in.
Supplicating TFD link
Pleading TFD link
Beseech TFD link
Entreat TFD link
Implore TFD link