Beat the egg in a small bowl and whisk it with a fork.
Mix flour, yeast, sugar and salt in a mixing bowl. Knead well with butter, milk and only half of the beaten egg with the dough hooks. The dough should be loosened from the bowl and be elastic. Add some flour if it sticks.
Cover the dough and let it rest for 30 - 45 minutes.
Preheat the oven to 400° F bottom and top heat.
Knead the dough well again and divide it into as many pieces as mini sausages are in the packaging. For me it was 28 pieces.
Wrap the sausages with the dough and knead well so that the dough does not tear when baking.
Place the mini Hot Dogs on a baking tray with a sheet of baking paper.
Brush them with the remaining egg.
Then bake the Hot Dogs for about 10 - 12 minutes in the oven. Take care that they do not get too dark.