Stir the yeast and sugar into 1 cup warm water. Let sit for 5 minutes or until puffy.
Add the flours, salt, olive oil, and the water-yeast mixture to a medium bowl. Stir with a wooden spoon to bring the dough together, then use clean hands to knead slightly to incorporate all of the flour. (Add a little extra water if needed if the dough is dry.) Cover with a clean towel and let rise for 1 to 2 hours or until about doubled in size. It should look puffy.
Divide the dough into 8 even sections. (I use a paring knife to cut it in half, then in half again and again, etc to make a pinwheel shape with 8 even triangles.)
Working with one piece of dough at a time, coating with flour as needed if sticky, flatten into a disc that’s about 6 inches wide. (It doesn’t need to be precise!)
Place 1 teaspoon pizza sauce and 2 heaping tablespoons each minced broccoli and cheese into the center. Sprinkle with a little Parmesan.
Fold in the dough to enclose the fillings. The seams should press and hold together with a little gentle pressing. Use a little water if needed to help secure the dough.
Place pocket onto a lined baking sheet and use a fork to poke a few holes in the top of each to allow steam to escape. Optional: Brush with olive oil and sprinkle with oregano.
Repeat to make all 8 pizza pockets. Set aside and cover with a towel while the oven preheats.
Preheat the oven to 400 degrees F. Bake the pizza pockets for 20 to 22 minutes or until firm to the touch. Let cool slightly and serve warm.
