"And surely, too, someone must have noticed that "With One Look" contains the single most inept line in a modern musical theatre song:
"With one look
I play ev'ry part!"
I don't think there is any ambiguity to this at all. I think it clearly means that she feels she can get into any character to such an extent that she could reveal that character with just one look. Remember, it is what she believes, not necessarily the truth, nor necessarily the definition of good acting. This is silent pictures. All she has to work with is her face and what she has been made to believe.