Proof the yeast by combining the yeast, sugar, and 1/4 cup of the water in a small bowl.  Let it stand until foamy, 5 to 10 minutes.   

Place 4-1/2 cups flour, the salt, and baking powder in the bowl of a food processor fitted with a dough blade or mixer with a dough hook.  Mix to blend.  Add the yeast mixture, milk, yogurt, egg, 2 tablespoons vegetable oil, and remaining 3/4 cup of water.  Knead the dough until smooth and elastic, 2 to 3 minutes in a processor, 5 to 8 minutes in a mixer, or to 8 to 10 minutes by hand.  The dough should be soft, but not too sticky: add additional flour as needed.

Place the dough in a large lightly oiled mixing bowl, turning the dough to coat all sides with oil. Cover the bowl with plastic wrap, then a clean kitchen towel, and let rise in a warm, draft-free place until doubled in bulk, 1 to 1-1/2 hours.      

Punch down the dough and divide into 8 even pieces. Roll them between your palms into smooth balls. Place the balls on a lightly floured baking sheet and cover with a slightly damp clean kitchen towel. Let rise until doubled in bulk, 40 to 60 minutes.

Preheat the Hōmdoor to 450 degrees F.

Roll out a dough ball on a lightly floured work surface or cutting board to form a flat disk about 6 inches in diameter.  Roll and stretch one end to make the traditional teardrop shape.  Using a pastry brush, brush off any excess flour.  Repeat the process for the remaining dough balls.

Drape a naan over the gaddi.  Reach your hand with the gaddi into the Hōmdoor and press the naan quickly onto the hot clay wall. Cook the naan until the top is puffed, blistered, and browned, 1 to 2 minutes. Using the bread tool with the flat end, gently pry the bread off the Hōmdoor wall, taking pains not to scratch the clay.  Simultaneously, catch the bread with the hooked bread tool so it doesn’t fall into the coals.  This may feel awkward at first, but with a little practice, you’ll make naans like a pro.  And once you get the hang of it, you can cook several naans at once.  Brush the tops of the naans with ghee or melted butter and place in a cloth-lined basket for serving. Serve hot.