"ponder, turn over in one's mind," 1873, perhaps from a figurative use of mull (v.) "grind to powder" (which survived into 19c. in dialect), from Middle English mullyn, mollen "grind to powder, soften by pulverizing," also "to fondle or pet" (late 14c.), from Old French moillier and directly from Medieval Latin molliare,mulliare, from Latin molere "to grind," from PIE root *mele- "to crush, grind."
Of uncertain connection to the mull (v.) defined in Webster's (1879) as "to work steadily without accomplishing much," and the earlier identical word in athletics meaning "to botch, muff" (1862). Related: Mulled; mulling.
"sweeten, spice, and heat (a drink)," c. 1600, of unknown origin. Perhaps from Dutch mol, a kind of white, sweet beer, or from Flemish molle a kind of beer, and related to words for "to soften." Related: Mulled; mulling.
"promontory" (in Scottish place names), late 14c., perhaps from Old Norse muli "a jutting crag, projecting ridge (between two valleys)," which probably is identical with muli "snout, muzzle." The Norse word is related to Old Frisian mula, Middle Dutch mule, muul, Old High German mula, German Maul "muzzle, mouth." Alternative etymology traces it to Gaelic maol "brow of a hill or rock," also "bald," from Old Celtic *mailo-s (source also of Irish maol, Old Irish máel, máil, Welsh moel).