For the bagel with honey-nut butter, put the flour in a bowl and mix with yeast and sugar. Stir in a little milk and let stand for about 15 minutes. Then add the remaining ingredients and knead everything into a smooth, supple dough. Let the yeast dough rise in a warm place for about 2 hours.
When the dough has doubled in size, form about 12 dumplings and make a hole about 3 cm wide in the center with the handle of a wooden cooking spoon. Let the rings rise for another 10 minutes. In a pot, bring about 4 liters of water with 2 tablespoons of sugar to a boil. Put the rings (max. 4 pieces at a time) into the boiling water, turn them over after 1 minute and let them steep for 3 minutes. Remove the rings with a slotted spoon and let them drain on a cake rack.
Preheat the oven to 200°C. Place the bagels on a baking tray lined with baking paper and brush with the egg yolk. Bake for 30 minutes. Let cool and serve with honey-nut butter.For the honey-nut butter, finely chop the hazelnuts, toast briefly and let cool. Meanwhile, in a bowl, cream the butter with the honey. Stir the cooled hazelnuts into the butter mixture. Pour the honey-nut butter into a bowl and leave to infuse for half a day.