Place the raspberries and water in saucepan and simmer for about 10 minutes.
Add sugar, bring to boil. Reduce heat and simmer an additional 5 minutes
Dissolve arrowroot in water, add to raspberries and simmer one minute. Remove from heat and allow to cool
Preheat oven to 325 degrees
Combine chickpea flour, almond flour, and sugar in large mixing bowl. Cut in butter until mixture resembles course sand.
Separate eggs, set white aside. Add yolks and water to mixture and stir until just combined. If dough feels sticky, chill for 20 minutes.
On a lightly floured surface, roll half of the dough into a sheet 1/8 inch thick. With a 2 inch cookie cutter, cut as many circles from the sheet as you can. Knead the leftover scraps of dough into a ball and roll it out again into a 1/8 inch sheet. Cut out more circles. You should now have about 10-12 circles. Place on parchment lined cookie sheet.
Repeat the rolling and cutting process with the other half of the dough, but cut out the center of each circle with a 1/2 inch cookie cutter. Use the dough from the centers to cut out more cookies.
spread a thin coating of the raspberry mixure in the center of each round on the cookie sheet. place a cut out cookie on top. Spoon a dab of raspberry into the opening. Repeat with each cookie. Brush cookie tops with egg white.
Bake cookies in preheated oven until light brown, 10 to 15 minutes