If baking in the kitchen, preheat the oven to 425°F.
In a large bowl, mix the crumbled yeast and honey in lukewarm water. Let the mixture stand for about 5 minutes to activate the yeast.
In another large bowl, whisk together the flour and salt. Make a well in the center and pour in the yeast mixture and ¼ cup of olive oil. Knead the dough with your hands or a stand mixer until smooth and elastic. If the dough is too sticky, add a little more flour. Cover the bowl with a clean kitchen towel and let the dough rise in a warm place for about an hour, or until doubled in size.
While the dough is rising, you can prepare the topping. Finely chop the parsley, chives, and green onions. Mince the garlic cloves.
In a medium bowl, combine the sour cream, remaining olive oil, herbs, garlic, paprika, salt, and pepper. Set aside.
Wash the zucchini and cut into thin slices or small pieces.
Punch down the risen dough and roll it out on a lightly floured surface into a flat, rectangular shape. Spread the sour cream mixture evenly over the dough. Sprinkle the zucchini on top and generously top with shredded cheese. If desired, sprinkle with additional paprika or black pepper.
If grilling, preheat your grill. If using a grill with a lid, you can bake the bread directly on a pizza stone or in a grill pan. Bake the zucchini grill bread until the cheese is melted and lightly browned and the crust is golden, usually about 15 minutes on the grill or slightly longer in the oven. Cooking time may vary depending on the thickness of the dough.
Let the finished grill bread cool slightly, then cut into pieces and serve warm. It's great as a side dish or as a main course with a salad. Enjoy!