For the basic bagels recipe, first put flour and salt in a suitable bowl and make a dent in the center. Stir the yeast and sugar together and empty into the indentation. Dust with a little flour. Let rest in a warm place for ten to fifteen minutes until small cracks form on the surface.
Slightly heat the milk water and let half of the butter melt in it. Add to the flour and knead all together to form a rather moist, smooth dough. Cover and let rise in a warm place until doubled.
Divide dough into even pieces (about 60 g each). Roll into finger-thick sticks on lightly floured surface and form rings. Press ends well to smooth. Let rest on floured surface for ten minutes.
In a wide frying pan, bring the water to a boil. Dip two or three dough rings at a time in it for about thirty seconds, until they have risen a little. If you leave them in the water longer, they will lose their shape. Remove the bagels with a skimmer, let them drain and place them on a baking sheet lined with parchment paper.
Melt the remaining butter and mix it with the egg yolk. Brush the bagels with it and sprinkle with your choice of hail salt, sesame seeds, poppy seeds, sunflower seeds, flax seeds and/or oatmeal, or just leave them plain.
Bake the bagels in the oven heated to 220 degrees on the second rack from the bottom for 20 to 25 minutes until light brown.