Step 1: Combine flour, sugar, and 1/4 tsp salt in medium bowl. Cut in butter with pastry blender or fork until pea size. Add 3 Tbsp ice water, stirring until mixture just comes together. If necessary, add up to 1 more Tbsp ice water. Form dough into ball, flatten into disk, and wrap in plastic. Chill 30 minutes.
Step 2: Heat oven to 350F. Roll dough into large round, about 10 1/2" diameter. Place in 9" tart pan with removable bottom, trimming excess dough.
Step 3: Whisk eggs and brush crust with 2 Tbsp of the mixture (reserve remainder for filling). Bake until golden, about 15 minutes.
Step 4: Combine carrots and milk in small saucepan while crust cooks. Bring mixture to a simmer over medium-high heat, reduce heat to low, and continue simmering until carrots are tender and milk has reduced to about 1/4 cup, about 10 minutes.
Step 5: Transfer mixture to food processor and puree until smooth.
Step 6: Whisk remaining egg mixture, yolk, sugar, and 1/4 tsp salt in medium bowl until pale and fluffy. Add buttermilk, vanilla, and carrot puree and whisk until combined. Strain through fine mesh strainer and pour into crust.
Step 7: Bake until carrot mixture sets but is still slightly jiggly in center, 16 to 20 minutes. Cool completely, then chill until set.
Step 8: Toss carrot ribbons with sugar, place on top of tart in center, and sprinkle with pistachios.
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