Use the mixing bowl from your mixer. Add the water and yeast and mix with a spoon until the yeast has dissolved. Let it rest for 5-6 minutes until the yeast becomes foamy.
Add the rest of the ingredients to the mixing bowl (the hard wheat flour, all-purpose flour, sugar and salt). Beat them, using the hook attachment, on medium/high. It should take about 7-8 minutes until if forms a soft, elastic dough, which is easy to handle. The dough will start to pull off the bottom.
Grease the whole interior of a bowl with oil. Transfer the dough to the bowl, cover with plastic wrap. Allow to rest for 30 minutes to 1 ½ hours, until it doubles in size.
Fill a bowl with water (500g). Add the sugar and mix until the sugar dissolves. Add the sesame to a separate bowl.
Brush some oil on to a clean work surface before setting down the dough. Cut in to about 10 pieces, 80 g each.
Form smooth balls. Knead each ball by hand, in to a long roll (like a sausage). Bring the two edges together to form a circle. Try to make them all the same size and shape.
Dip each bagel into the bowl with water and directly into the bowl with sesame seeds.
Place on to 35x40 cm baking sheets that have been lined with parchment paper. Bake for about 15-20 minutes, until golden.
To serve, brush with melted butter while they are still hot. Try them with blue cheese, feta cheese or pickled grapes!!.