Heat the oil in a large skillet over medium-high heat. Add the celery, garlic, onion, 1 teaspoon salt, and a few grinds of pepper and cook, stirring occasionally, until golden, about 6 minutes.
Remove the skillet from the heat, add the vodka, return to the heat, and tip the pan to ignite on a gas flame (or light with a stick lighter). Let the flames cook off, about 1 minute. Stir in 1/2 cup water, the capers and brine, horseradish, Worcestershire and tomatoes and cook, covered, over medium heat, stirring once in a while, until the tomatoes are soft, about 20 minutes. Remove the lid and continue cooking for an additional 2 minutes. Season with salt and pepper. Keep the sauce warm while cooking the pasta.
Add the pasta to the boiling water and cook according to package directions. Drain the pasta and toss with the sauce. Serve sprinkled with the Parmesan and celery leaves.
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