Mix together warm water, inulin and yeast in a small bowl and cover with cling film and a towel (or silicone mat) to keep warm. Transfer to a nice warm spot until yeast activates and is foamy (15-20 mins).
Add cheese and cream cheese to mixer. Chop 5 sec/speed 5. Scrape down sides of bowl.
Melt cheese 3 min/90°C/speed 3.
Add eggs and baking powder; mix 15 sec/speed 3. Scrape down sides of bowl.
Add remaining ingredients; mix 30 sec/speed 3. Then knead 2 min/dough setting.
Transfer dough to a silicone mat.
Roll dough into a ball until it is no longer sticky. Cut into 8 pieces. Roll each piece into a ball. Push a finger through the centre of each ball and using your fingers gently widen the hole while pressing and shaping the outer edge to be smooth and even. (Alternatively roll into a long sausage and join each end to form a bagel).
Transfer bagels to a lined baking tray. Cover with a silicone mat and allow to rest in a warm place for 1 hour.
Preheat oven to 170°C.
Baste with egg yolk and season.
Bake bagels for 15-20 minutes or until lightly golden and cooked through.