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Special equipment: a muffin pan with 12 (1/2- or 1/3-cup) muffin cups.
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Make cups: Preheat oven to 375F.
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Cover stack of phyllo with 2 overlapping sheets of plastic wrap and a dampened kitchen towel.
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Put 1 phyllo sheet on a work surface and brush with some butter, then top with 2 more sheets of phyllo, brushing each with butter.
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Cut buttered stack into 6 (4 1/2-inch) squares with a sharp knife, trimming sides as needed.
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Line each of 6 muffin cups with a square.
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Make 6 more phyllo cups (4 are extra, in case of breakage) in same manner with remaining pastry sheets and butter.
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Bake cups in middle of oven until golden, about 8 minutes, then cool completely in pan on a rack.
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Make filling: Increase oven temperature to 400F.
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While cups are cooling, melt butter in a 3-quart heavy saucepan over moderately low heat, then whisk in flour.
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Cook roux, whisking, 3 minutes.
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Add milk in a stream, whisking, and bringto a boil, whisking.
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Reduce heat and simmer, whisking occasionally, 5 minutes.
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Remove from heat and whisk in mustard, yolks, and 1/4 cup Parmigiano-Reggiano until combined, then fold in goat cheese.
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(Cover surface of mixture with wax paper if not using immediately.)
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Beat egg whites in a large bowl with an electric mixer until they just hold stiff peaks.
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Fold one third of whites into sauce to lighten, then fold in remaining whites gently but thoroughly.
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Spoon batter into 8 phyllo cups and sprinkle with remaining Parmigiano-Reggiano.
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Bake in middle of oven until souffles are puffed and golden, about 15 minutes.
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Make salad while souffles bake: Whisk together vinegar, mustard, and salt in a bowl, then add oil in a slow stream, whisking until emulsified.
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Just before souffles are ready, toss frisee and radishes in a large bowl with just enough dressing to coat.
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Mound salad onto 8 plates and sprinkle with chives, then make a small nest in center of each.
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Place a souffle cup in each salad and serve immediately.
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Cooks' notes: Phyllo cups can be made 1 day ahead and kept in pan, carefully wrapped in plastic wrap, at room temperature.
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Souffle filling (without egg whites) can be made 1 day ahead and chilled, covered.
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Bring to room temperature and stir (to loosen) before proceeding.
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You can make the souffles 4 hours ahead (keep at room temperature).
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Put in a 375F oven for 8 minutes to reheat.
