Preheat the oven to 350°. In a medium saucepan, combine the carrots with the zest and juice and 1/4 cup of water. Season with salt and bring to a boil. Cover and simmer over moderate heat until the carrots are very soft, about 30 minutes. Discard the zest. Transfer the carrots and any liquid to a blender and puree until very smooth.
Meanwhile, in a large saucepan of boiling salted water, cook the pasta until al dente. Drain the pasta, reserving 1 cup of the cooking water.
Return the pasta to the pot. Add the reserved water and the carrot puree and cook over moderate heat, stirring frequently, until the pasta is coated with a thickened sauce, about 5 minutes. Stir in three-fourths of the cheese and cook, stirring, until very creamy, 2 to 3 minutes longer. Stir in the tarragon and season with salt and white pepper.
Transfer the pasta to a medium baking dish and top with the remaining cheese. Bake until the cheese is melted and lightly browned, about 20 minutes. Let stand for 5 minutes before serving.