In a large saucepan of boiling, salted water, cook the macaroni until al dente, about 5 minutes. Drain, shaking off excess water.
Brush four 12 cup, non-stick mini muffin tins with butter. Sprinkle with 2 tablespoons of the Parmigiano; tap out the excess.
In a large saucepan, melt the 1 1/2 tablespoons of butter. Whisk the flour over moderate heat for 2 minutes. Whisk in the milk and cook, whisking, until boiling, about 5 minutes. Add the cheddar and American cheeses and whisk until melted. Off the heat, whisk in the egg yolk and paprika. Fold in the macaroni.
Spoon slightly rounded tablespoons of the macaroni into the prepared muffin cups, packing them gently. Sprinkle the remaining 2 tablespoons of Parmigiano on top.
Bake the mini macs in the upper and middle thirds of the oven for 10 minutes, until golden and sizzling. Let cool for 5 minutes. Using a small spoon, carefully loosen the mimi macs, transferring to a platter and serve.
Can be prepared ahead up to baking. Refrigerate overnight, then bake as above.