Heat olive oil in a heavy pot over high heat. Sprinkle short ribs on both sides with salt and pepper. Quickly sear both sides of the short ribs, using tongs to flip them halfway through. (Just sear about 1 1/2 minutes per side.) Remove the shortribs to a plate.
Pour wine and beef broth into the pot. Add rosemary. Stir to combine, scraping the bottom of the pot to deglaze. Return the shortribs to the pot, reduce heat to low, then cover the pot and simmer it for 2 1/2 to 3 hours. (You can also put the pot into a 300 degree oven if you'd prefer not to simmer on the stovetop.).
After they have cooked, carefully remove the shortribs from the pot again. Stir in mustard, cream, and capers, then raise the heat and allow it to bubble up and gently boil for a good couple of minutes, or until it has thickened a bit. Taste and add more salt and pepper if needed. Return the shortribs to the sauce, put on the lid, and turn off the heat.
To roast the mushrooms, preheat oven to 400 degrees. Arrange the mushrooms in a single layer on a baking sheet. Drizzle with olive oil and sprinkle with salt and pepper, then roast the mushrooms until they're golden brown, about 15 to 20 minutes.
Serve the shortribs on top of the mushrooms, then drizzle with extra cream sauce. Add a little rosemary sprig if you want to be fancy.
This is absolutely divine.