Season the beef: 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. Place in a deep pan and cover; refrigerate for at least 16 hours and up to 36.
Make the sauce: Melt 1 tbsp 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 2 cups of 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 tbsp 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; allow to cool, and refrigerate for at least 16 hours and up to 2 days.
Roast the beef: Remove the beef from the refrigerator and let sit at room temperature for one hour before roasting (take the sauce out at the same time as well). 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.
Finish the gravy: Once done, the beef will need to sit for at least 20 minutes, during which time you can finish the gravy – pour out all but 2 tbsp of fat from the roasting pan; heat the pan over medium heat (using two burners if needed). Pour in the remaining 1 cup of beef broth, whisking regularly – once heated, add the wine sauce and whisk to incorporate (if the sauce is too thick, add a slurry by whisking 1 tbsp flour with 1/4 cup warm water).
To serve: slice the beef tenderloins into 1-inch slices, and serve with gravy on the side.