Binge is both a verb, and a noun, it's meaning is the same in both. For a noun you'd use it like this 'He went on a binge and couldn't drive home' in this case, we don't need to mention that he drank too much alcohol, by saying he couldn't drive home and saying he went on a binge, it is implied that the reason he can't drive home is because he drank too much. For a verb you'd use it like this (Which you already know how to use!) 'I binged on Ice Cream'

First, if you only had one beer, it isn't a binge. One beer is a drink. Binging requires at least 6 beers and you really probably shouldn't call it a "binge" until you've had more than 12 beers. The word "binge" implies both large quantities and a loss of control. One beer is neither of those things. But yes, you can say "I binged on chocolate" if you ate an entire large box (or three) of chocolate. You could also say "I am binge drinking," if you are on your 9th drink and trying to explain your brilliant plan for you and the bartender to change clothes with each other right there in the middle of the bar.