Green’s Dictionary of Slang

a large, high hat.

1607		Tourneur Revenger’s Tragedy (1967) I ii: He made a goodly show under a penthouse, And when he rid his hat would check signs And clatter barbers’ basins.
1611		J. Cook Greenes Tu Quoque Scene ix: Uds foote, shall I be confin’d all the dayes of my life to walke under a pent-house?
c.1698		B.E. Dict. Canting Crew n.p.: Pentice Nab, a very broad-brim’d Hat.
1725		New Canting Dict. n.p.: penthouse-Nab a very broad-brim’d Hat.
1737, 1759, 1760, 1776		Bailey Universal Etym. Eng. Dict. [as cit. 1725].
c.1750–1882		B.M. Carew Life and Adventures.
1785, 1788, 1796		Grose Classical Dict. of the Vulgar Tongue n.p.: penthouse nab, a large hat.
1806–7		J. Beresford Miseries of Human Life (1826) 101: Your left eye sorer than ever [...] since he first took shelter under your ‘pent-house lid’.
1811		Lex. Balatronicum.
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue.
c.1850		Duncombe New and Improved Flash Dict. n.p.: Penthouse-nab a broad-brimmed hat.