Special equipment: a waffle iron and meat mallet
For the sweet potato waffle: Preheat the oven to 200 degrees F.
Whisk together the all-purpose flour, whole-wheat pastry flour, baking powder, baking soda and 1/2 teaspoon salt in a large mixing bowl. Reserve.
Put the butter in to a small saute pan and set over medium heat. Cook the butter until foam has formed on top and then subsided, and browned bits begin to appear in the bottom of the pan, about 5 minutes. Remove the pan from the heat and allow to cool slightly.
Meanwhile, whisk together the buttermilk, sweet potato puree, brown sugar, egg and egg whites in a medium mixing bowl. Once the butter has cooled slightly, add it to the sweet potato mixture and whisk until well combined.
Add the wet ingredients to the dry ingredients and stir with a wooden spoon or rubber spatula until just combined. Do not overmix. Allow the mixture to rest for 5 minutes while you preheat a waffle iron.
Preheat a waffle iron according to the manufacturer's directions. Spray the waffle iron with cooking spray. Scoop a scant 2/3 cup of the rested batter into the center of the waffle iron and press down to close the top. Cook according to the manufacturer's directions until golden brown and just cooked through, 3 to 5 minutes, depending on waffle iron model. (Please make sure to read the directions that come with the machine.) Remove the cooked waffle onto a baking sheet set over a cooling rack and place in a warm oven. Repeat this process with the remaining batter to make 5 additional waffles.
For the crispy chicken: Set an oven rack in the upper third of the oven and preheat it to 375 degrees F.
Remove the tenderloin from each chicken breasts and save for another future use. Cut each chicken breast in half crosswise on a large plastic cutting board. One at time, place a large piece of plastic wrap on top of a piece of chicken and use a meat mallet to gently pound the chicken until it is 1/2 inch thick. Put the chicken into a large mixing bowl with the buttermilk, cover with plastic wrap and refrigerate for 1 hour.
In a mixing bowl or large baking dish, whisk together the rice flour, garlic powder, onion powder, paprika, 2 teaspoons salt and 2 teaspoons pepper. In a second mixing bowl or large baking dish, whisk together the egg whites and hot pepper sauce.
In batches, coat the chicken pieces with the flour mixture, turning to dust both sides and tapping off any excess. Dip into the egg white mixture, turning to coat both sides and allowing any excess to drip off. Then dip back into the rice flour mixture, making sure to coat all sides.
Heat a large skillet over medium heat with 1 tablespoon of the canola oil. In batches, cook the breaded chicken, turning once, until lightly browned and just cooked through, about 5 minutes total, adding additional oil between batches. Remove the cooked chicken to a cooling rack set over a baking sheet.
Sprinkle a generous amount of the grated Gruyere on top of each piece of chicken. Bake until the cheese is just melted, about 5 minutes.
For the raspberry and tomatillo jam: Put the raspberries, tomatillos, sugar and lemon juice in a small saucepan and stir to combine. Bring to a simmer over medium heat and cook until the raspberries have completely broken down, the tomatillos are softened and the mixture has reduced by at least one-third, about 15 minutes. Pour into a medium mixing bowl and allow to cool completely. The jam will thicken as it cools.
For the club sandwiches: Heat a large nonstick saute pan over medium heat and spray with cooking spray. In batches, cook the quail eggs until the whites are set, but the yolks are still runny, about 1 minute.
Cut each hot waffle into 4 equal pieces. Top 1 piece of waffle with a few spinach leaves, 1 piece of chicken, 1 piece of waffle smeared with the raspberry and tomatillo jam on both sides, a few more spinach leaves, 1 piece of chicken, 2 quail eggs and top with 1 piece of waffle. Sprinkle with a light dusting of confectioners' sugar. Repeat this process to make 7 additional sandwiches.