Heat a large skillet over medium-high heat with olive oil. Add the ground beef and cook until fully browned, breaking it up gently as it cooks. Once nicely caramelized, transfer the beef to a plate and set aside.

In the same skillet, lower the heat slightly and add the butter. Once melted, add the onion and cook until soft and translucent.

Add the mushrooms and cook slowly, allowing them to release their moisture. Continue cooking until the moisture evaporates and the mushrooms begin to turn lightly golden.

Stir in the garlic and thyme and let them cook briefly, just until fragrant, about 30 to 60 seconds.

Pour in the white wine and gently scrape the bottom of the pan to release any flavorful bits. Let it simmer for a couple of minutes, until the alcohol cooks off.

Return the ground beef to the skillet, then stir in the Dijon mustard, heavy cream, and water. Cover the pan and let it simmer for 6 to 8 minutes, until the sauce turns smooth and creamy.

Stir in the Parmesan, then season with salt and black pepper to taste. Once everything is well blended and creamy, remove the skillet from the heat.