Heat a sauté pan over medium, melt butter, add carrots and onion, sprinkle with a pinch of salt, and cook, stirring gently and frequently, until mixture begins to caramelize, about 30 minutes. Stir in minced thyme and cook another 1-2 minutes then remove from heat.

 In a small saucepan over medium-high heat melt the butter. Add the onion and garlic and cook 3-4 minutes until soft. Whisk in the flour until incorporated and simmer for 1-2 minutes until thickened. Stirring constantly, whisk in the pan juices, red wine, Worcestershire sauce, mustard, and thyme sprigs and bring to a boil, stirring constantly. Mixture will thicken slightly. Reduce heat to maintain a slow simmer and cook uncovered until mixture reduces by about 25% (about 10-15 minutes). Season to taste with salt and pepper, strain, return to pan and keep warm over very low heat until ready to use.

 Preheat oven to 400°. Lightly toast rolls then spread inside of each with mayonnaise. Divide the meat between the rolls and top each with ¼ of the onion/carrot mixture and 2 slices of Havarti cheese. Wrap each sandwich in aluminum foil and heat in oven for 10 minutes or until cheese melts. Divide jus between 4 small bowls and serve with the sandwiches, dipping into jus before each bite.