Previous studies highlighted Brettanomyces claussenii as a versatile yeast that produces ethanol or acetic acid from lactose, or selectively metabolizes glucose while leaving behind galactose, depending on different operational conditions. This flexibility enables the production of galactose-rich bioproducts from liquid dairy residues. The purpose of this study is to: (i) optimize the anaerobic fermentation of milk permeate (MP) by B. claussenii to maximize the yields of galactose and ethanol and minimize leftover glucose, and (ii) combine the optimized process with distillation and drying and characterize its multiple products. Response surface methodology was used for the optimization. Three fermentation parameters were chosen as input factors: temperature (25–35 °C), inoculation level (7.0–8.5 log cfu/mL), and time (4–40 days), with three metabolites as responses: galactose, glucose, and ethanol. The optimal combination of parameters resulted in temperature, 28 °C; inoculation level, 7.6 log cfu/mL; and time, 33 days. Under these conditions, the fermented product was predicted to have 63.6 g/L galactose, 4.0% v/v ethanol, and 0 g/L residual glucose. The optimal parameters were used to run 18 L fermentations followed by distillation and freeze-drying. As a result, four product streams were obtained and characterized for relevant physicochemical and nutritional attributes. Our results show that the partial fermentation of MP by B. claussenii can be the first step to develop lactose-free, low-in-glucose, galactose-rich bioproducts, which improve the value of this residue and broaden its applications in the food supply chain.