For the dough: In a large bowl, dissolve the sugar in 3/4 cup very warm water. Sprinkle the yeast over the water and let it sit until bubbling and slightly frothy, 5 to 10 minutes. Add the whole wheat flour, all-purpose flour, olive oil and salt, and mix well by hand. Place the dough in the bowl of a stand mixer fitted with a dough hook, and mix on medium speed until the dough is a tight, shiny ball that no longer sticks to the sides of the mixing bowl, about 6 minutes. Alternatively, transfer the dough ball to a floured surface and knead by hand, about 10 minutes. Cover with a damp towel and place the bowl in a warm place until doubled in size, 1 hour. Divide the dough into 8 pieces and form each into a 2- to 3-inch diameter ball. Place on a clean baking sheet and let the dough rise again for 45 minutes.
For the filling: Heat a large nonstick saute pan over medium-high heat. Add the spinach and 1/4 cup water and cook until the spinach is wilted, dark green and reduced in volume to about 1 cup, about 5 minutes. Transfer the spinach to a medium bowl and cool for 3 to 5 minutes. Squeeze out any excess moisture with your hands. Stir in the cheese, tuna, salt and pepper.
Preheat the oven to 425 degrees F and move a rack to the middle of the oven.
Flour a work surface and roll each ball into a 4- to 5-inch disk. Place 1 heaping tablespoon of filling on half of a circle and fold over to enclose the filling, forming a half moon. Pinch the dough together along the edge so that it is completely sealed, and then place on a baking sheet. Repeat for the remaining dough and filling. Bake until golden brown, 17 to 20 minutes, turning the pan halfway through. Cool 5 minutes before serving.
This recipe makes about 2 cups of filling.
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