Combine the sugar and water in a small, heavy saucepan and cook over medium heat, stirring until the sugar is dissolved. Increase the heat to high and cook without stirring until the mixture turns amber. Quickly divide among 6 (4-ounce) ramekins and let cool.
Combine the carrot juice and carrots in a medium saucepan, bring to a boil over medium heat, and decrease the heat to a simmer. Cook for about 10 minutes, or until tender. Pour into a blender and puree until smooth. Strain the pureed carrots through a sieve and return to the saucepan with the cream and vanilla. Heat over medium heat until bubbles form around the edges of the pan.
Preheat an oven to 250°F. Combine the eggs, egg yolks, and sugar in a large bowl and whisk until the mixture is pale yellow and forms a slowly dissolving ribbon when dropped from the whisk onto the surface. Gradually whisk the warm carrot mixture and salt and pepper into the eggs and divide the custard among the ramekins. Place the ramekins in a baking pan and add water to the baking pan to come three-fourths of the way up the sides of the ramekins. Cover the pan with aluminum foil and bake for about 1 1/2 hours, or until firm. Remove from the oven and water and let cool. Refrigerate for at least 4 hours or as long as overnight.
For the vinaigrette: Whisk the vinegar, mustard, and tarragon together in a small bowl until well combined. Gradually whisk in the olive oil, then the salt and pepper.
To serve, run a knife around the edge of each ramekin and invert a flan onto each plate. Dress the arugula and carrots with the vinaigrette and serve alongside the flan.
Serves 6 as a first course.
Reprinted with permission from ©Marin Magazine, Organic Marin: Recipes from Land to Table, by Tim Porter and Farina Wong Kingsley, published by Andrews McMeel click for book review
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