An Etymological Dictionary of the German Language/Grütze
Grütze, f., ‘groats, grit, brain,’ from MidHG. grütze, ‘water-gruel’; a variant of the equiv. MidHG. griuȥe (griutze?); OHG. gruzzi (whence Ital. gruzzo, ‘pile of collected things’); comp. AS. grŷt and grytt, E. grit and groat (from AS. *grota?), OIc. grautr, Du. grut, gort, ‘groats.’ From OG. the Romance cognates, Fr. gruau, ‘groats,’ are derived. Besides Grieß, MidHG. grûȥ, ‘grain,’ is also allied to Grütze; hence ‘grain’ may be the prim. meaning of the Teut. root grū̆t, with which the primit. cognates Lith. grúdas, ‘grain, kernel,’ and OSlov. gruda, ‘clod,’ are also connected.