Put the meat into the hot oven to roast for 15 minutes. Turn the oven heat down to 350 degrees Fahrenheit after that. Bake for about 45 more minutes until the core reaches 150 degrees. Remove the beef and let it rest under foil for 15 minutes.

Mash your soft butter with a fork in a clean bowl. Stir in your horseradish, fresh chives, salt, and pepper until fully mixed. Split your French bread loaf in half lengthwise with your knife. Spread a thick layer of this seasoned butter on both open sides.

Place your cheese slices on the top half of the buttered bread. Combine more butter, sliced red peppers, and salt in your skillet. Sauté over medium heat until the peppers are soft and not crunchy. Turn off the stovetop heat and set the skillet aside.

Place your dirty roasting pan with the pan drippings on the stovetop. Add your chopped red onion, butter, thyme, and salt to the pan. Cook over medium heat until the onions become very soft and translucent. Pour in your beef broth and bring it to a simmer.

Scrape up all the browned bits from the pan bottom using a spoon. Strain this hot liquid through your fine mesh sieve into clean cups. Slice your rested beef across the grain as thinly as you can. Keep the meat covered with foil so it stays warm.

Toast your buttered bread halves in the oven at 350 degrees. Bake for 10 to 15 minutes until the cheese melts completely. Arrange your warm beef slices on the bottom piece of the loaf. Top the meat with your cooked warm sweet peppers.

Cover the sandwich with the top cheesy piece of French bread. Slice the large loaf diagonally into six equal sized sandwich portions. Serve each warm sandwich with a small cup of hot dipping sauce. Enjoy your delicious homemade meal immediately with your friends.