How to Make It
In a saucepan, melt the butter. Add the onion and cook over moderate heat, stirring, until starting to brown, 10 minutes. Add the sugar, garlic, thyme and bay leaves and cook over moderately low heat, stirring, until the onion is deep golden, about 20 minutes. Add the port and simmer until nearly absorbed, 2 minutes. Add the broth, vinegar and Worcestershire and simmer over moderate heat until reduced to 2 cups, about 30 minutes. Strain the jus into a saucepan and season with salt and pepper.
Preheat the oven to 325°. Heat the oil in an ovenproof skillet. Season the meat with salt and pepper and sear until well browned all over. Add the butter, garlic and thyme and baste the meat for 1 minute. Transfer to the oven and roast for 30 minutes, basting every 5 minutes, until an instant-read thermometer inserted in the center of the meat registers 128°; transfer to a rack set over a baking sheet and let rest for 20 minutes. Add the broth to the skillet and scrape up any browned bits. Boil until reduced by half; strain into the jus and skim off any fat.
In a food processor, blend the egg yolks, vinegar and a large pinch each of salt and pepper for 90 seconds. With the machine on, add the oil in a slow, steady stream. Transfer to a bowl, stir in the horseradish and season with salt and pepper.
In a skillet, cook the shallot and garlic in 1 tablespoon of the butter, until softened. Add the spinach and season with salt. Cook, tossing, until just wilted; transfer to paper towels to drain.
Preheat the broiler. Thinly slice the beef. Arrange the baguettes on 2 baking sheets and spread with the aioli. Spoon the spinach over the bottom halves and top with the beef and cheese. Broil until the cheese melts.
Turn the oven to 425°. Reheat the jus. Close the sandwiches, brush with the remaining melted butter and weight down with a baking sheet and heavy skillet. Bake for 10 minutes; remove the weighted baking sheet and bake for 5 minutes. Serve with the jus.
You can substitute 1 cup of mayonnaise for the egg yolks in the aioli; cut the canola oil to 1/2 cup. Banyuls vinegar is an aged sweet wine vinegar from the south of France. Cave de L'Abbé Rous makes a very good version; it's available from amazon.com.