This study evaluated the effects of different roasting profiles (time/temperature) and brewing methods on the physicochemical and sensory characteristics of coffee brews. Cold brewing (dripping and immersion) and hot brewing (French press) methods were studied to understand the effects of water temperature and technical brewing method conditions on the chemical compound extraction in coffees roasted at high-temperature short time (HTST) and low-temperature long time (LTLT). The results showed that coffee beverages were clearly differentiated concerning the roasting profile when hot water was used (90 ± 3 °C) in brewing. Separation of beverages according to the water temperature used in brewing was observed. Notably, hot brewing coffees were distinguished from cold brewing (19 ± 2 °C) based on a higher titratable acidity and abundance of some furan compounds. The non-volatile extraction rate increased at higher brewing temperatures. At the same brewing temperature, dripping exhibited a higher extraction rate than immersion brewing, which suggests that the coffee extraction process is affected by the design and operation of the cold brewing system. Coffee beverages brewed with HTST and cold dripping displayed the highest value in total dissolved solids (TDS), extraction yield, as well as the highest caffeine, trigonelline, 4- and 5-caffeoylquinic acids (CQAs) contents. Regardless of the roasting profile, coffees brewed by cold dripping were perceived with more bitter and roasted flavors. In contrast, cold immersion and hot coffee beverages showed remarkable sweetness, nutty, caramel, and malt attributes. In turn, these attributes showed an inverse correlation with caffeine concentration, trigonelline, CQAs, and TDS. The findings of this study demonstrate that volatile and non-volatile compounds present in roasted coffee depend on time-temperature roasting conditions; in turn, their presence in the resulting beverages are related to the extraction of the operational conditions of coffee brewing methods.