In a large saucepan over high heat on the stove, warm 2 tablespoons oil. Add the carrot, celery, and onion and cook until the vegetables begin to brown, 6 to 8 minutes, stirring occasionally. Add the garlic and cook for about 2 minutes, stirring occasionally. Reduce the heat to medium, add the tomato paste and cook for about 2 minutes, stirring occasionally. Add the broth, wine, vinegar, bay leaves, rosemary, and ½ teaspoon of pepper. Mix well. Bring to a boil over high heat. Reduce the heat to medium-low and let simmer for 45 minutes to blend the flavors.
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Strain the liquid through a sieve into a medium saucepan, pressing down on the solids with the back of a spoon. Simmer over medium heat until about 180 milliliters of liquid remains, about 45 minutes more. Reduce the heat to very low. Add the butter 1 tablespoon at a time, whisking to help melt each piece into the sauce. Season with salt and pepper. Remove the sauce from the heat.
Allow the roast to stand at room temperature for 30 to 45 minutes before grilling. Lightly brush the roast all over with oil and season with the herbes de Provence and salt and pepper.
Prepare the grill for indirect cooking over medium heat (180° to 230°C).
Prepare the grill for cooking over medium heat (200°C).
Brush the grilling grates clean. Grill the roast over indirect medium heat, with the lid closed, until cooked to your desired doneness, 1½ to 1¾ hours for medium rare (start checking with an instant-read thermometer after 1¼ hours). Transfer the roast to a cutting board, loosely cover with aluminum foil, and let rest for 10 to 20 minutes. Meanwhile, warm and whisk the sauce over low heat. Carve the beef and serve warm with the sauce.
Brush the grilling grates clean. Grill the roast over medium heat, with the lid closed, until cooked to your desired doneness, 1½ to 1¾ hours for medium rare (start checking with an instant-read thermometer after 1¼ hours). Transfer the roast to a cutting board, loosely cover with aluminum foil, and let rest for 10 to 20 minutes. Meanwhile, warm and whisk the sauce over low heat. Carve the beef and serve warm with the sauce.
