In a small bowl, place yeast, 1 teaspoon sugar, and lukewarm water. Allow to sit around 10 minutes, until it becomes foamy on top.
In small bowl, mix vegetable oil, oregano, and garlic. Allow to sit for a few minutes while the yeast proofs.
In a large bowl or stand mixer fitted with the whisk attachment, mix together 1 ½ cups flour, salt, and sugar. After the water-yeast mixture has become foamy, add to flour mixture along with oil-oregano-garlic mixture. Combine thoroughly.
Add another 1 cup of flour and eggs and mix until smooth. Switch to the dough hook attachment if you are using a stand mixer.
Add another 1 ½-2 cups of flour, mixing thoroughly, and then remove from bowl and place on a floured surface. Knead remaining ½ cup flour into dough, continuing to knead for 3-4 minutes until smooth and elastic.
Place dough in a greased bowl and cover with damp towel. Allow to rise at least 3 hours.
Combine spinach, feta, 1 egg, lemon juice, and lemon zest in a bowl.
Roll out dough into a large rectangle about ¾ inch thick. Spread an even layer of spinach- feta mixture all over the surface of the dough, leaving a small border around the edges.
9. Roll into a log the long way and pinch the ends. Using a serrated knife, slice into around 12 pieces and place in a greased 9x12 Pyrex or baking dish. Allow to rise again 45–60 minutes.
Beat 1 egg in a small bowl. Brush tops of rolls with egg wash. Sprinkle with 2 tablespoons grated Parmesan, 1 teaspoon lemon zest, and a sprinkle of thick sea salt.
Preheat oven to 375°F. Bake for 20-25 minutes, until golden brown on top and middles do not seem mushy. Serve warm.