Step 2

Prepare the braised oxtails: Preheat the oven to 300º. In a 6-quart Dutch oven, heat the vegetable oil over medium-high heat. Season the oxtails liberally with salt and pepper, then sear, turning as needed, until golden brown, 8 to 10 minutes. Transfer the oxtails to a plate.

Step 3

Add the celery, carrots and onions to the pan, and cook until golden, 5 to 7 minutes. Add the garlic and cook until fragrant, 1 to 2 minutes more. Pour in the red wine, stirring constantly to deglaze the pan, then return the oxtails to the pan and add the chicken stock, thyme and rosemary. Bring to a simmer, then cover and transfer to the oven. Cook until the oxtails are tender, 2½ to 3 hours. Raise the oven to 350º.

Step 4

Meanwhile, make the red onion gastrique: In a 10-inch skillet, heat the vegetable oil over medium-high heat. Add the red onion and cook until lightly caramelized, 5 to 6 minutes. Stir in the garlic and cook until fragrant, 1 to 2 minutes. Add the sugar and red wine vinegar to the pan, and bring to a simmer. Cook until reduced to a syrup, 16 to 18 minutes, then set aside.

Step 5

Make the caramelized onions and mushrooms: In a 10-inch skillet, heat the vegetable oil over medium-high heat. Add the mushrooms and cook until golden brown, 4 to 5 minutes. Add the onions to the pan and continue to cook until caramelized, 6 to 8 minutes. Stir in the butter to coat and season with salt and pepper.

Step 6

Assemble the French dip sandwiches: Once tender, remove the oxtails from the pan and place in a bowl. Once cool enough to handle, pick apart the meat and transfer to a medium saucepan, discarding the bones and any cartilage. Strain the remaining contents of the pot, reserving the liquid and discarding the vegetables. You should have 3½ cups of braising liquid; keep warm.

Step 7

To the saucepan with the picked oxtail meat, add 1½ cups of the braising liquid. Bring to a simmer over medium heat and cook until the liquid has reduced to a glaze on the meat, 16 to 18 minutes. Stir in half of the red onion gastrique, adding more to taste. Season with salt and pepper.

Step 8

On a baking sheet, open and lay out the toasted hoagie rolls. Divide the braised oxtail between the rolls, then divide the onions and mushrooms over the oxtail. Top each sandwich with 2 slices of Havarti cheese and place in the oven. Bake until the cheese has melted, 4 to 5 minutes. Press each sandwich closed, then halve crosswise and serve alongside the braising liquid for dipping.