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Bring a few quarts of heavily salted water to a rolling boil. Add the pasta. While the pasta cooks, start the sauce.
Melt the butter over medium-high heat in a big skillet. Once the butter has melted, turn heat down to medium and add the shallots, garlic, 1/2 teaspoon salt and the peppercorns. Sauté until just fragrant, about 2 minutes. Add in the champagne and crank the heat up to high to bring to a boil. Add 1/2 cup of the starchy pasta cooking water and boil for 5 minutes.