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1
Make the sauce: in a large saucepan over high heat, warm the olive oil; add in carrots, celery, and onion; cook until the vegetables begin to brown, 6-8 minutes, stirring occasionally.
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2
Add in garlic; cook for 2 more minutes, stirring occasionally.
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3
Decrease heat to medium, add in tomato paste; cook about 2 more minutes, stirring occasionally.
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4
Add in broth, wine, vinegar, bay leaves, rosemary, and 1/2 teaspoon pepper; mix well.
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5
Bring to a boil over high heat, then decrease heat and let simmer 45 minutes.
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6
Strain sauce through a sieve into a medium saucepan, pressing down on the solids with the back of a spoon.
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7
Continue to simmer until about 3/4 cup of liquid remains, about 45 more minutes.
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8
Add the butter 1 tablespoon at a time, whisking to melt them.
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9
Season with salt and pepper to taste; remove sauce from heat.
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10
Let beef stand at room temperature 30-45 minutes before grilling; lightly brush or spray the roast all over with oil and season with the herbes de Provence, and salt and pepper to taste.
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11
Grill beef over Indirect Medium heat until cooked to desired doneness, 1 1/2-1 3/4 hours for medium rare, but start checking with an instant-read thermometer after 1 1/4 hours.
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12
Transfer the beef to a cutting board, loosely cover with foil; let rest for 10-20 minutes.
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13
Meanwhile, warm the sauce over medium heat; carve the beef and serve warm with the sauce.
