In a 3- to 4-quart pan over high heat, bring about 1 quart water to a boil. Peel carrots, cut into 1/2-inch slices, and add to water. Cover and return to a boil, then reduce heat and simmer until carrots are tender when pierced, 10 to 12 minutes. Drain.
Meanwhile, gently fit pastry into a 1 1/2-inch-deep, 9-inch pie pan. Fold under any excess pastry at rim and decoratively flute edge. Prick pastry with a fork several times. Bake on the bottom rack of a 350° oven until pastry is golden, 13 to 15 minutes.
Mash cooked carrots and measure 1 1/2 cups. Reserve any extra carrots for another use.
In a blender, combine the 1 1/2 cups carrots, milk, honey, eggs, cinnamon, ginger, salt, and cloves; whirl until very smooth.
Set pie pan on a foil-lined baking sheet on bottom rack of oven. Carefully pour carrot mixture into pastry. Bake until filling barely jiggles in the center when pie is gently shaken, 50 to 55 minutes. If crust rim starts to get too dark, drape affected areas with foil.
Cool pie on rack at least 1 hour. Serve warm or cool. If making up to 1 day ahead, cover and chill.