flour, dough, noodles
麵 centers on wheat-based food products: flour, dough, and the noodles made from them. The common thread is ground grain turned into edible forms.
麵 combines 麥 (wheat) and 面, which likely contributes the sound. The character originally referred to wheat flour and by extension dough and noodles.
Wheat (麥) is ground into a fine face (面) of powder: flour. From flour comes dough, and from dough come noodles.
For メン, imagine men kneading dough to make noodles: men -> メン, and the wheat (麥) becomes the noodles they eat.