In a small bowl, combine the olive oil, thyme, fennel, caraway, 1 Tbs. salt, and 1-1/2 tsp. pepper. Pat the tenderloins dry with paper towels and coat them with the spice mixture, using your hands to spread it evenly; it will sparsely cover the meat.
Melt 1 Tbs. of the butter and the oil in a 10-inch skillet over medium heat.
Add the mushrooms, shallot, sugar, and 1/4 tsp. salt. Cook, stirring often, until soft and beginning to brown, about 6 minutes.
Add the thyme, peppercorns, and half of the wine. Simmer briskly until the wine reduces and just covers the solids, 10 to 15 minutes.
Add the remaining wine and reduce again until the wine just covers the solids, 10 to 12 minutes more.
Add the beef broth and simmer until reduced by half, about 15 minutes. Strain through a fine sieve set over a 1-quart measuring cup, pressing lightly on the solids. If you have more than 1-1/2 cups liquid, return the sauce to the pan and simmer until reduced to 1-1/2 cups
Melt the remaining 1 Tbs. butter in a 1-quart saucepan over low heat. Whisk in the flour and cook, whisking often, until smooth and light beige in color, about 1 minute.
Slowly add the wine reduction, whisking constantly. Bring to a simmer and cook, whisking often, until slightly thickened, about 3 minutes. Season to taste with salt and pepper.
If you've seasoned the beef ahead of time, remove it from the refrigerator and let sit at room temperature for about an hour before roasting. Meanwhile, position a rack in the center of the oven and heat the oven to 375°F.
Arrange the roasts on a flat rack on a large rimmed baking sheet. Roast until an instant-read thermometer inserted in the center reads 120°F for rare , 125°F to 130°F for medium rare, or 135°F for medium, 40 to 50 minutes.
If the sauce was made ahead, heat gently in a small saucepan over medium-low heat, whisking a few times, until barely simmering.
Meanwhile, let the beef rest for 15 minutes before carving crosswise into thick slices. Slice only as much as you plan to serve right away (leftovers keep better unsliced). Spoon the sauce over each serving or pass at the table.