Preheat oven to 400 degrees F.
Toss mushrooms, garlic, 1 tablespoon oil, 1/4 teaspoon pepper, 1 teaspoon sage, 1 teaspoon thyme and 1/2 teaspoon salt in a large bowl. Transfer to a roasting pan and roast in the oven for 5 minutes. Stir and continue roasting until the mushrooms are soft and fragrant, 5 to 10 minutes more. Set aside to cool.
To butterfly tenderloins, lay one tenderloin on a large cutting board. Holding the knife blade flat, parallel to the board, make a lengthwise cut through the center of the meat, stopping short of the opposite edge so that the flaps remain attached. Open up the flaps as you would open a book. Cover with plastic wrap. With a meat pounder, rolling pin or heavy pan, pound the meat to an even 1/4-inch thickness. Butterfly and pound the remaining tenderloin.
Divide the mushroom mixture between the tenderloins, spreading evenly and leaving a 1-inch border all around. Starting with a long side, roll up each tenderloin to enclose the filling, then tie the roasts at 2-inch intervals with kitchen string. Combine the remaining 2 teaspoons pepper, 1 teaspoon sage, 1 teaspoon thyme and 1 teaspoon salt in a small bowl. Rub the mixture all over the tenderloins.
Increase oven temperature to 450 degrees F.
Heat the remaining 1 tablespoon oil in a large, heavy, ovenproof skillet over medium-high heat. Add the roasts, bending to fit if necessary, and cook, turning often, until the outsides are browned, 3 to 5 minutes total.
Transfer the pan to the oven and roast, checking often, until the internal temperature reaches 145 degrees F, 15 to 20 minutes. Transfer the roasts to a cutting board, tent with foil and let rest for 5 minutes. Remove the string, cut the pork into 1-inch-thick slices and serve with Tomato Salsa Verde on the side.
Tomato Salsa Verde
1 vegetable, 3 lean meat, 1 fat