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Using a Y-shaped vegetable peeler, shave asparagus into very thin ribbons to equal 1 cup. Shave the purple carrots (from multicolored carrots) into very thin ribbons to equal 1/2 cup. Shave remaining carrots into very thin ribbons to equal 1/2 cup. (Reserve remaining asparagus and carrots for another use.) Set aside.
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Cook pasta in a pot according to master technique (until very al dente, about 3 minutes shorter than package directions call for).
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While pasta cooks, place purple carrot ribbons in a fine wire-mesh strainer. Lower strainer into boiling water with pasta, and cook carrots until tender, about 20 seconds. Remove strainer; drain carrots, and set aside. Melt 1 tablespoon butter in a large skillet over medium. Add garlic; cook, stirring often, until fragrant, about 1 minute. Add 1/4 cup water; let come to a simmer. Gradually whisk in 5 tablespoons butter, one piece at a time, waiting until butter is nearly melted before adding the next piece. Stir in salt.
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Using tongs, lift cooked pasta from pot and transfer to skillet, reserving cooking liquid in pot. Increase heat under skillet to medium-high. Add snap peas, asparagus ribbons, uncooked carrot ribbons (do not add purple carrot ribbons), and remaining 6 tablespoons butter; cook, stirring and shaking skillet constantly, adding 1/4 cup reserved cooking liquid at a time, until a creamy sauce forms and clings to pasta, 2 to 3 minutes.
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Remove skillet from heat. Add pea shoots, cheese, chives, tarragon, and lemon zest and juice, stirring constantly until thoroughly combined and cheese is melted. (Add a little more cooking liquid if necessary to maintain a creamy consistency.)
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Remove skillet from heat. Add pea shoots, cheese, chives, tarragon, and lemon zest and juice, stirring constantly until thoroughly combined and cheese is melted. (Add a little more cooking liquid if necessary to maintain a creamy consistency.)
