Preheat the oven to 450 degrees F. Pulse the carrots, celery and shallots in a food processor until coarsely chopped.
Heat 1 tablespoon of the olive oil in a large nonstick skillet over medium high. Add the chopped vegetables and cook, stirring frequently, until light golden and soft, 8 to 10 minutes. (Add a splash of water if the mixture begins to stick.) Add the ground beef and 4 teaspoons of the tomato paste and cook, breaking the mixture up with a wooden spoon, until browned, about 4 minutes. Add 1/2 cup water, the parsley, raisins, 1 tablespoon of the vinegar and 3/4 teaspoon salt. Bring to a simmer and cook until most of the water is absorbed and the mixture gets saucy, about 1 minute. Let cool slightly.
Meanwhile, toss the pepper halves with the remaining 1/2 tablespoon oil in a microwave-safe bowl. Cover with plastic wrap and microwave until the peppers are pliable, 10 to 12 minutes. Carefully uncover the bowl and pour out any liquid that has accumulated.
Stir the couscous into the beef mixture. Whisk together the remaining 2 tablespoons tomato paste, 1 tablespoon vinegar and 3/4 cup water in the bottom of a large baking dish.
Carefully transfer the peppers to the baking dish cut-side up and fill each pepper with the couscous mixture. Sprinkle with the cheese. Cover with foil and bake until the peppers are tender and the stuffing is hot, 20 to 25 minutes. Serve warm or at room temperature drizzled with the tomato cooking liquid.
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