If you've never made caramel or creme brulee, you should watch a video of cooking sugar to caramel. I've linked to a video in the notes.
In a stainless steel sauce pan, cook the sugar with ¼ cup of water on medium high heat until the sugar melts and turns to caramel. Turn the hood vent on, or open a window as there may be a little smoke. This is something you need to watch closely as it cooks, but don't stir it too much.
As the sugar slowly changes color from light brown to amber, turn the heat down and swirl the pan to help melt any clumps. If the mixture clumps don't worry, it will melt eventually after you add the cream.
When the caramel is amber colored, but not too dark, add the butter and melt. It will sizzle a lot. Remove the pan from the heat and add the brandy and cook for a minute to evaporate the alcohol. If you have a gas burner the pan may ignite-this is natural so don't worry.
Add the cream, mushrooms, and whisk to incorporate, The heat and reduce the sauce until thickened to your liking.
If it’s too thick, add a tablespoon of water at a time to loosen it. The sauce will keep for a couple weeks in the fridge. As it chills it will firm and solidify. To refresh it you can microwave it briefly to make it loose again.
Notes
Mushrooms
You can crumble the mushrooms for a little texture in the sauce, or grind them to a fine powder in a spice grinder to a smooth sauce.
How to serve
You can use this anywhere you'd use a simple caramel sauce. It's great over ice cream, bread pudding, or spooned over a simple chocolate cake.
Making caramel
If you haven't cooked sugar into caramel before you should get familiar with the process. It cooks at a high temperature and you don't want to get it on yourself. Don't be scared though, it's easy once you get the hang of it. Video Suggestion:How to Caramelize Sugar