Preheat the oven to 425°. In a large saucepan of boiling salted water, cook the macaroni until al dente, about 5 minutes. Drain, shaking off the excess water.
Brush four 12-cup, nonstick 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 in 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 about 10 minutes, until golden and sizzling. Let cool for 5 minutes. Using a small spoon, carefully loosen the mini macs, transfer to a platter and serve.