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Preheat oven to 350 degrees.
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Line standard muffin tin with 12 paper liners.
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In heavy-bottom deep 2-quart saucepan over lowest heat, whisk together eggs and sugar. Add butter and white chocolate, stirring until melted and smooth. Mixture should be warm, not hot.
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Add flour, baking powder and salt, beating until smooth. Scrape down sides of pan once or twice. Add chocolate and stir to create a marble effect as it melts. Do not over-blend; you want the marbling.
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With large spoon, fill cupcake papers three-fourths full with batter. Bake 18 to 23 minutes, until tops are lightly browned around edges and cake tester inserted in center comes out clean.
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Cool in pans 5 minutes, then transfer to rack to cool completely; cupcakes will sink slightly.
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When cool, cut top off each cupcake. With large end of melon baller, remove a rounded scoop of cake from lower section of each cupcake. Using a #100 (very small) ice cream scoop or the melon baller, fill each cupcake with a nice little round scoop of ice cream.
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Replace cupcake top, press down a bit to adhere the two sections, then wrap sandwich style in waxed paper or parchment.
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Place 6 cupcakes in each of two 1-gallon plastic freezer bags and freeze. Keeps 2 months; serve frozen.