Step 1Rinse the sorrel leaves under cold running water, then remove the tough stems. Drain on paper towels and spin the leaves in a salad spinner. Heat the oven to 350 degrees.
Step 2Saute the shallot in the butter in a large skillet or saucepot until tender, 1 to 2 minutes. Add the sorrel and cook until the leaves are wilted and turn olive green, about 1 minute.
Step 3Spoon the sorrel into a blender. Add the milk and puree until smooth.
Step 4In a large bowl, beat the eggs with a wire whisk just until well blended. Add the whipping cream and stir to combine. Add the sorrel mixture, salt and pepper and stir to combine.
Step 5Divide the sorrel mixture among 7 (3-ounce) buttered ramekins. If you do not have enough ramekins, you can bake the flans in batches. Place the ramekins in a large shallow pan and add warm water to come halfway up the sides of the dishes.
Step 6Bake until the flans are just set in the center and are puffed and slightly pulled away from the sides, about 45 to 50 minutes. Remove them from the oven and the water bath to a wire rack to cool slightly.
Step 7To serve, run a knife around the edge of each ramekin to loosen the edges and invert it onto a serving plate. Sprinkle the top of each flan with finely minced chives.