Add the tomato paste and cook to concentrate the flavors slightly, stirring and scraping often, 1-2 minutes. Add the sugar and red pepper flakes and cook for about 1 minute, reducing heat to medium-low if the bits sticking to the pan start to get dark.

Add the red wine and balsamic vinegar, and scrape up any browned bits in the bottom of the pan. Adjust heat as needed to maintain a gentle simmer and cook uncovered until the liquid is reduced to 1-1 1/4 cups, 20-30 minutes.

In another medium saucepan, melt the butter over medium heat. Add the flour and whisk to make a smooth paste. Cook, whisking frequently, until the paste is pale gold and smells lightly toasted, about 2 minutes.

Whisk the beef broth and red wine reduction into the roux paste and continue simmering, whisking occasionally, until sauce has thickened and reduced to about 2 cups, 30-40 minutes. The flavor should be nicely concentrated.

Meanwhile, slice the reserved mushroom caps very thin.

Heat the butter in a large frying pan over medium heat. Add the reserved shallot and saute until soft and fragrant, about 3 minutes.

Add the sliced cremini caps and saute, stirring and scraping frequently, until mushrooms are tender and juices are brown and start to stick to the pan, about 15 minutes. Be sure to scrape the pan often as the mushroom juices form.

Pour a little red wine sauce into the mushrooms and stir to loosen any browned bits, then add the mushroom mixture to the red wine sauce.

Whisk in the Worcestershire, Parmesan, and butter. Season to taste with salt and pepper. Set aside, or refrigerate for up to 3 days.

Preheat the oven to 275°F.

If the beef tenderloin isn't already trimmed, use a chef's knife to carefully cut off the fat and silver skin. (Silver skin is the shiny connective tissue that runs the length of much of the meat.) Cut the garlic into very thin slices. With a sharp paring knife, cut a slit into beef and slide in a garlic slice. Be sure the slit is deep enough to accommodate the whole slice. Repeat to distribute garlic evenly over the tenderloin.

Rub the tenderloin all over with the kosher salt.

If the beef is not yet tied, cut 8-12 pieces of kitchen twine long enough to wrap around the meat. Tie the roast with the twine at even intervals, tight enough to help the meat hold its shape.

Rub the roast with the oil, season with the pepper, and then tuck the thyme and rosemary sprigs into the twine, evenly distributing them all over the roast. Transfer to a baking sheet.

Roast the meat on middle rack of oven until medium-rare (the thickest part of roast should read 135°F on an instant-read thermometer), about 1 hour.

Check to see that meat is done. Remove from oven or add time as needed.

Let the roast rest for 10 minutes. Gently reheat the Red Wine Mushroom Sauce. Snip the kitchen twine from beef and remove. Slice the beef and arrange on a platter. Scatter parsley on top and serve with sauce on the side.