Rinse and dry the roast, meat should be at room temperature. use a sharp paring knife to make slits over the entire surface of the roast and insert garlic slivers.
In a small bowl mix together the thyme leaves, savory, oregano, 1 1/2 teaspoons of salt, 1/2 teaspoon pepper and 3 tablespoons of the oil. Brush this mixture on all sides of the roast.
Place oven rack in center position and preheat oven to 450 F.
Lightly oil or spray the bottom of a roasting pan, place roast in the center of the pan, fat side up. Roast in the oven for 15 minutes.
While meat is roasting prepare the vegetables. Oil or spray a large rimmed baking sheet. Peel onion and cut into wedges, leaving the root end intact. Toss onions, potatoes, and mushrooms in a large bowl with 1/2 cup olive oil. Season with fresh ground pepper and Kosher salt, toss again, then place on the prepared baking sheet.
After meat has roasted for 15 minutes, reduce heat to 350 F and place the pan of vegetables on the lower rack of the oven. Continue to roast the meat for 50-60 minutes or until meat thermometer registers 130-135 F. Stir the vegetables every 15 minutes, until slightly browned and charred around the edges, for 50-60 minutes.
When done, transfer the roast to a cutting board and let rest for 20 minutes. At this time if the vegetables are not fork tender, continue to roast until done. Remove vegetables and tent with foil.
Skim off and discard any fat from pan. Place pan over medium heat on stovetop, add broth and wine to deglaze the pan. Bring mixture to a simmer and reduce by half. Swirl in the butter and season with salt and pepper.
Cut roast crosswise against the grain into 1/4? slices. Arrange sliced meat on platter and surround with roasted vegetables. Drizzle sliced meat with some of the pan gravy and serve remainder to pass.
Notes
I added the broth and wine to the roasting pan, loosened any bits and transferred to a saucepan as I found that easier to work with.Also, I used winter savory and oregano because I still have it growing outside. You can just use 2 teaspoons of dried thyme or substitute your own favorite herbs.