Flash brewed coffee is typically done with lighter roasted, fruity or floral coffees. Simply because this brewing method brings out the aromatics and gentle notes in the coffee. It's also recommended that you don't skimp on the type of coffee you use for flash brewing, as flash brewing will emphasize on your coffee's flaws.
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In comparison, cold brewed coffee have a heavier, more viscous mouthfeel. It tends to have lesser aromatics and acidity which is what draws some people to it. A simple side by side test with the same beans will show you the striking difference.
Flash brew is a fresh cup of coffee that should be consumed as it's brewed. Where else with cold brew, it is possible to brew large amounts and store them for a couple of weeks. If you like the taste of cold brew you can freeze it and consume it much later and shouldn't experience much change in the flavours.
In the coming blog posts, i'll share the Chemex & Aeropress method of flash brewing.