Dissolve the yeast in warm water with honey; let stand for 5 minutes until foamy. Stir in olive oil, then gradually mix in flour and salt until a shaggy dough forms. Knead on a floured surface for about 6 minutes until smooth and elastic—about 8-10 minutes by hand, or use your mixer with the dough hook.
Place dough in an oiled bowl, cover with a damp towel, and let rise at room temperature for 30–45 minutes until nearly doubled. While it rises, mix together the ricotta, mozzarella, feta, garlic, and half of the oregano. Season lightly with salt and pepper (taste first—feta can be salty).
Preheat your oven to 475°F for at least 20 minutes before baking. If using a pizza stone or steel, let it heat through as well. Lightly flour your work surface.
Gently deflate the dough and transfer to your prepared surface. Using your hands (not a rolling pin), press and stretch into a rough circle about 12-13 inches in diameter—thin edges are fine; they'll crisp up nicely.
Spread the cheese mixture evenly over the dough, leaving about ½ inch around the edge. Sprinkle with remaining fresh oregano. If you prefer more garlic, add an extra clove or two at this point.
Transfer to your preheated stone or slide onto a baking sheet (if using the latter, lightly oil the sheet). Bake for 12-14 minutes until edges are golden and cheese is bubbly with brown spots. The crust should be firm but still pliable when you lift it—underbaking leads to soggy centers.
Let cool on a wire rack for 5 minutes before slicing. This helps the cheese set slightly so slices hold together better than if served immediately off the stone. Serve warm, with extra oregano and a drizzle of olive oil on top.
