Place water and yeast in warm mixing bowl and let stand for 2 minutes. Add sugar and bean puree and mix until incorporated.
Add butter, chickpea flour and salt. Mix until incorporated. Add bread flour and begin mixing on low speed until flour is completely absorbed and dough is starting to pull away from the sides of the bowl. Turn up to medium speed and let the dough work for about 5 minutes. Dough should be dry enough to make a ball as it kneads.
Pour dough onto a floured surface and cut into 2-3 ounce balls. Let the balls rise (covered) for about 20 minutes.
As dough is almost ready, fill a large stock pot or sauce pan with about half a gallon of water (should be at least 3 inches deep), stir in the honey and bring water to a simmer.
Poke a hole in the center of the dough balls with your thumb and shape into a bagel shape. Drop into the simmering water. Simmer on both sides for about 3 minutes. Remove from water and place on a greased baking sheet. If desired, season bagels with salt, sesame seeds, herbs or other spices.