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1.
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Preheat oven to 350F.
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2.
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To prepare crust: Lightly coat a 9- to 10-inch tart pan with oil.
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Place all-purpose flour, whole-wheat flour, tarragon and 1/2 teaspoon salt in a food processor; pulse to combine.
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Add butter one piece at a time, pulsing once or twice after each addition, until incorporated.
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Add 1/4 cup oil and 1/4 cup yogurt and pulse just until the dough starts to come together.
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Transfer the dough to the prepared pan (it will be crumbly), spread evenly and press firmly into the bottom and all the way up the sides to form a crust.
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3.
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Bake the crust until set but not browned, about 15 minutes.
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Let cool on a wire rack.
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4.
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To prepare filling: Heat 2 tablespoons oil in a large skillet over medium heat.
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Add onion and cook, stirring occasionally, until tender, about 5 minutes.
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Stir in carrots and 1 tablespoon sherry (or rice vinegar) and cook, stirring, for 2 minutes.
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Remove from the heat.
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Spread mustard over the crust.
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Sprinkle with Cheddar, then evenly spread the carrot mixture in the tart shell.
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5.
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Whisk 1/2 cup yogurt, milk, eggs, tarragon, the remaining 1 tablespoon sherry (or rice vinegar), 1/4 teaspoon salt and pepper in a medium bowl.
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Place the tart pan on a baking sheet and pour in the filling.
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Bake the tart until the filling is firm and the edges are golden brown, 40 to 45 minutes.
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Let cool for 15 minutes before slicing.
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Serve warm or chilled.
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* Ingredient note: Sherry is a type of fortified wine originally from southern Spain.
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Dont use the cooking sherry sold in many supermarketsit can be surprisingly high in sodium.
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Instead, purchase dry sherry thats sold with other fortified wines in your wine or liquor store.
