Saute the sliced mushrooms in butter until browned and fully cooked. Set aside on a paper towel lined plate to drain and cool.
In a small saucepan over medium low heat, whisk the Better than Bouillon Beef base with the heavy whipping cream. Add a dash (just a few drops) of worcestershire suace and whisk to incorporate. At this point you should taste the sauce - you do not want the worcestershire to be overpowering, and want to have a distinctly beefy flavor from the beef base. Now is the time to adjust if you wish to add more of anything.
Whisk in corn starch to thicken the sauce - you can omit this step, or add additional corn starch to your liking, however too much corn starch may produce a flavor of it's own.
As your burgers are cooking, melt on your slice of swiss cheese. Toasting your burger buns is optional but recommended.
Top your burger with mushrooms to taste, and drizzle with at least one Tbsp of sauce per burger. Spreading the sauce on your bun will allow for a more even, less drippy coverage of sauce.