A stabilized bran component and a stabilized whole grain wheat flour containing the component are produced by subjecting a bran-enriched coarse fraction which contains bran, germ and starch to grinding or milling to reduce grittiness of the coarse fraction without substantially damaging the starch due to abrasion. The coarse fraction may be stabilized by heating to substantially reduce the lipase and lipoxygenase activity of the coarse fraction without substantial gelatinization of the starch. High levels of natural antioxidants and vitamins are retained while avoiding substantial acrylamide formation during the stabilization. The stabilized coarse fraction or stabilized bran component may be combined with a fine fraction which contains predominantly endosperm to obtain a stabilized whole grain wheat flour. The stabilized whole grain wheat flours and the stabilized bran component exhibit extended shelf life and may be used for making baked goods, such as cookies, with desirable oven spread, and a non-gritty mouthfeel.