Parsing inflected forms may not always work as expected. If the following does not give the correct word, try Latin Words or Perseus.
monstrōsē, monstrōsus, v. monstruose, monstruosus.
monstrŭōsus (post-class. mon-strōsus), a, um, adj. [monstrum], strange, preternatural, monstrous (class.): monstruosissima bestia, of the ape, Cic. Div. 2, 32, 69: hominum partus monstrosi, Luc. 1, 557: ferculum longe monstruosius, Petr. 69: scriptis monstruosus, Suet. Gram. 15: libidines, unnatural, id. Calig. 16: mulier si monstrosum aliquid aut prodigiosum enixa sit, Paul. Sent. 4, 9, 3 (but in Cic. Fin. 1, 18, 61, instead of monstrosi the correct reading seems to be morosi; so B. and K.; v. Madv. ad h. l.).
Hence, * adv.: monstrŭōsē (monstrōsē), strangely, unnaturally, monstrously: cogitare, Cic. Div. 2, 71, 146.