An evil overlord dead because of a pretzel? Then the plot of Disgaea: Hour of Darkness happens.
More seriously, Goering had been the successor since 01/09/1939. I don't think there's any chance of a peace though; Churchill is not going to make peace with a country that has invaded half of Europe.
There are serious knock-on effects. The Battle of Britain is still won by Britain, and Goering gets much of the whispered blame for it. He won't have Hitler's level of authority over the other military leaders, and Barbarossa is likely to go straight for Moscow the next year. Depending on how much that affects the Soviet state (arguments endlessly rehashed in other threads, but I think it renders everything NW of there unholdable, and cripples state authority and planning capability, resulting in less industry) that may get Germany a compromise peace with a post-Stalin USSR.
If there's peace with the USSR, it's back to hitting Britain, perhaps in North Africa and Persia. If there isn't, then it's basically as historical with a slower Soviet rebound, due to the disruption of a more effective German 1941, and German retreats which are Mainstein's Backhand Blow instead of stand & die Fuhrerbefehl.