Mirror, Dynasty 18

Mirror with a Handle in the Shape of a Young Woman Holding a Papyrus Umbel
New Kingdom, Dynasty 18, reign of Thutmose IV, ca. 14001390 B.C.E.
Upper Egypt; Thebes
Bronze or copper alloy, H. 29 cm (11 7/16 in); diam. 15.5 cm (6 1/8 in) weight 1.2 kg (2.7 lbs)
Bequest of Walter C. Baker, 1972 (1972.118.30)

There are many examples of these mirrors, each with a papyrus branch and a woman:

The Brooklyn museum also has one

and OIM has two mirrors

The lady in the Met's example, in addition to the papyrus umbel serving as a crown, is also holding a papyrus. Why do all these mirrors have this symbol?

OIM 10203
The museum info card gives the meaning of the papyrus as "to be rejuvenated". Wilkinson explains the use of it as an amulet "as a symbol for 'green,' and for concepts such as 'flourish', 'joy,' and 'youth." (_Reading Egyptian Art_, page 123)

Those using the mirrors hope for youthful rejuvenation, and may have hoped the use of this symbol would aid in achieving it.

Queen Kawit, a wife of Mentuhotep II, is attended to on her sarcophagus, and has her mirror to inspect the hairdresser's work
The male attendant pouring the Queen a drink says, "For your ka, O mistress."
The KA is an aspect of the soul meaning vital life force.