Cut the mushrooms into thick slices (about 1/4 inch or 6mm). Cut shallot into small cubes, finely chop garlic (preferably with a knife and not using a garlic press). Roughly chop parsley.
Heat the oil in a large frying pan over medium-high heat. Add half of the mushrooms in an even layer, cook until browned at the bottom then turn over and cook until browned. Transfer to a plate and repeat with the remaining mushrooms.
Add butter and shallot to the pan. Cook over medium-low heat for 1-2 minutes, until softened. Add garlic and thyme and cook for 30 seconds, until fragrant.
Add flour and cook, whisking, for a minute.
Add wine and cook for 1-2 minutes, until mostly evaporated. Scrape all the brown bits at the bottom of the pan.
Add cream, broth, Dijon mustard, Worcestershire sauce, and lemon juice. Bring to a boil and cook over low heat for about 1-3 minutes, until thickened. The sauce can be just a little bit runny at this point, it will thicken further while cooling.
Add the mushrooms back to the pan and stir to combine.
Season the sauce with salt and pepper. Garnish with chopped parsley.