The Preparation
Heat olive oil and butter in a pan over medium-high heat.
Add sliced shallots and cook until translucent and softened.
Add the fresh thyme leaves and let them bloom briefly with the shallots.
Add all the sliced mushrooms. Cook for several minutes — they will soak up the butter/oil and then release their own liquid. Season with salt and pepper.
Once mushrooms have reduced in volume and released liquid, sprinkle about 1 tablespoon of flour over the mushrooms. Stir to coat — the flour will clump and absorb the liquid, which is what you want.
Add the dry vermouth and stir, letting it cook down.
Slowly stream in the heavy cream, stirring constantly, until you reach a thick, saucy consistency. Add cream gradually — you may not need all of it.
Taste and adjust seasoning. The sauce should be thick, rich, and coating the mushrooms.
Serve over pork chops, chicken, or any protein. Let the meat rest, then spoon the sauce over the top.